{"id":26846,"date":"2023-01-08T13:50:16","date_gmt":"2023-01-08T08:20:16","guid":{"rendered":"https:\/\/ccssanswers.com\/?p=26846"},"modified":"2023-01-09T09:44:04","modified_gmt":"2023-01-09T04:14:04","slug":"big-ideas-math-answers-grade-6-chapter-2","status":"publish","type":"post","link":"https:\/\/ccssanswers.com\/big-ideas-math-answers-grade-6-chapter-2\/","title":{"rendered":"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals"},"content":{"rendered":"<p>It is very tough to clear all the math exams without proper preparation. The solutions in <a href=\"https:\/\/ccssanswers.com\/big-ideas-math-answers-grade-6\/\">Big Ideas Math Answers Grade 6<\/a> Chapter 2 Fractions and Decimals are prepared by our highly-experienced subject experts after ample research and easy-to-understand concepts too. Thus the students are implied to answer all the questions while practicing and cross-check the solutions through Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals.<\/p>\n<h2>Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals<\/h2>\n<p>You guys are recommended to solve the Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals regularly &amp; attempt the exams with confidence. The topics covered in the Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals are designed perfectly &amp; in an understandable way. Tap the links and kickstart your preparation.<\/p>\n<p><strong>Fractions and Decimals<\/strong><\/p>\n<ul>\n<li>Fractions and Decimals STEAM VIDEO\/Performance<\/li>\n<li>Fractions and Decimals Getting Ready for Chapter 2<\/li>\n<\/ul>\n<p><strong>Lesson: 1 Multiplying Fractions<\/strong><\/p>\n<ul>\n<li>Lesson 2.1 Multiplying Fractions<\/li>\n<li>Multiplying Fractions Homework &amp; Practice 2.1<\/li>\n<\/ul>\n<p><strong>Lesson: 2 Dividing Fractions<\/strong><\/p>\n<ul>\n<li>Lesson 2.2 Dividing Fractions<\/li>\n<li>Dividing Fractions Homework &amp; Practice 2.2<\/li>\n<\/ul>\n<p><strong>Lesson: 3 Dividing Mixed Numbers<\/strong><\/p>\n<ul>\n<li>Lesson 2.3 Dividing Mixed Numbers<\/li>\n<li>Dividing Mixed Numbers Homework &amp; Practice 2.3<\/li>\n<\/ul>\n<p><strong>Lesson: 4 Adding and Subtracting Decimals<\/strong><\/p>\n<ul>\n<li>Lesson 2.4 Adding and Subtracting Decimals<\/li>\n<li>Adding and Subtracting Decimals Homework &amp; Practice 2.4<\/li>\n<\/ul>\n<p><strong>Lesson: 5 Multiplying Decimals<\/strong><\/p>\n<ul>\n<li>Lesson 2.5 Multiplying Decimals<\/li>\n<li>Multiplying Decimals Homework &amp; Practice 2.5<\/li>\n<\/ul>\n<p><strong>Lesson: 6 Dividing Whole Numbers<\/strong><\/p>\n<ul>\n<li>Lesson 2.6 Dividing Whole Numbers<\/li>\n<li>Dividing Whole Numbers Homework &amp; Practice 2.6<\/li>\n<\/ul>\n<p><strong>Lesson: 7 Dividing Decimals<\/strong><\/p>\n<ul>\n<li>Lesson 2.7 Dividing Decimals<\/li>\n<li>Dividing Decimals Homework &amp; Practice 2.7<\/li>\n<\/ul>\n<p><strong>Chapter: 2 &#8211; Fractions and Decimals<\/strong><\/p>\n<ul>\n<li>Fractions and Decimals Connecting Concepts<\/li>\n<li>Fractions and Decimals Chapter Review<\/li>\n<li>Fractions and Decimals Practice Test<\/li>\n<li>Fractions and Decimals Cumulative Practice<\/li>\n<\/ul>\n<h3><a id=\"Fractions_and_Decimals_STEAM_VIDEO\/Performance\"><\/a>Fractions and Decimals STEAM VIDEO\/Performance<\/h3>\n<p><strong>STEAM Video<\/strong><\/p>\n<p><strong>Space is Big<\/strong><\/p>\n<p>An astronomical unit (AU) is the average distance between Earth and the Sun, about 93 million miles. Why do astronomers use astronomical units to measure distances in space? In what different ways can you compare the distances between objects and the locations of objects using the four mathematical operations?<br \/>\nAnswer:<br \/>\nThe space beyond Earth is so incredibly vast that units of measure<br \/>\nwhich are convenient for us in our everyday lives can become GIGANTIC.<br \/>\nDistances between the planets, and especially between the stars,<br \/>\ncan become so big when expressed in miles and kilometers that they&#8217;re unwieldy.<br \/>\nSo for cosmic distances, we switch to whole other types of units:<br \/>\nastronomical units, light years and parsecs.<br \/>\nAstronomical units, abbreviated AU, are a useful unit of measure<br \/>\nwithin our solar system. One AU is the distance from the Sun to Earth&#8217;s orbit,<br \/>\nwhich is about 93 million miles (150 million kilometers).<\/p>\n<p><strong>Watch the STEAM Video \u201cSpace is Big.\u201d Then answer the following questions.<\/strong><br \/>\n1. You know the distances between the Sun and each planet.<br \/>\nHow can you \ufb01nd the minimum and maximum distances between<br \/>\ntwo planets as they rotate around the Sun?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27278\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-1.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 1\" width=\"194\" height=\"215\" \/><br \/>\nGiven the distances between the sun and each planet we<br \/>\ncan find the minimum and maximum approximately distances<br \/>\nbetween two planets around the sun, we have each<br \/>\nplanet distance now we will see which is farthest and<br \/>\nwhich planet is near to sun, then subtract the larger one<br \/>\nfrom smaller and tell the distances from them,<br \/>\nExample the distance from sun to mars is 5 AU and<br \/>\nsun to mercury is 2 AU,<br \/>\nthen the distance from mercury to mars is 5 &#8211; 2 = 3 AU.<\/p>\n<p>2. The table shows the distances of three celestial bodies from Earth.<br \/>\nIt takes about three days to travel from Earth to the Moon.<br \/>\nHow can you estimate the amount of time it would take to travel from<br \/>\nEarth to the Sun or to Venus?<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27279\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-2.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 2\" width=\"331\" height=\"91\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-2.png 331w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-2-300x82.png 300w\" sizes=\"(max-width: 331px) 100vw, 331px\" \/><br \/>\nEarth to the Sun \u2248 1190 days ,<br \/>\nEarth to Venus \u2248 330 days<\/p>\n<p>Explanation:<br \/>\nSpeed = Distance \u00f7 Time ,<br \/>\nWe have distance from Earth to Moon is 0.00256 and<br \/>\ntime is 3 days = 3 X 24 = 72 hours<br \/>\nnow speed is = 0.00256 \u00f7 72 = 0.0000355 AU per hour,<br \/>\nnow we have distance from Earth to Sun is 1 AU and speed as<br \/>\n0.000035 per hour, Time taken is distance by speed =<br \/>\n1 \u00f7 0.000035 = 28571.428 hours, now we divide by 24 to get days as<br \/>\n28571.428 \u00f7 24 = 1190.4 days \u2248 1190 days to travel from Earth to Sun,<br \/>\nnow we have distance from Earth to Venus as 0.277 Au and speed as<br \/>\n0.000035 per hour, Time taken is 0.277 \u00f7 0.000035 = 7914.28 hours,<br \/>\nnow we divide by 24 to get number of days as 7914.28 \u00f7 24 = 329.7 \u2248<br \/>\n330 days to travel from Earth to Venus.<\/p>\n<p><strong>Performance Task<\/strong><\/p>\n<p><strong>Space Explorers<\/strong><\/p>\n<p>After completing this chapter, you will be able to use the concepts you learned to answer the questions in the STEAM Video Performance Task.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27039\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-3.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 3\" width=\"293\" height=\"371\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-3.png 293w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-3-237x300.png 237w\" sizes=\"(max-width: 293px) 100vw, 293px\" \/><br \/>\nYou will use a table that shows the average distances between the Sun and each planet in our solar system to \ufb01nd several distances in space. Then you will use the speed of the Orion spacecraft to answer questions about time and distance.<br \/>\nIs it realistic for a manned spacecraft to travel to each planet in our solar system? Explain why or why not.<\/p>\n<h3><a id=\"Fractions_and_Decimals_Getting_Ready_for_Chapter_2\"><\/a>Fractions and Decimals Getting Ready for Chapter 2<\/h3>\n<p><strong>Chapter Exploration<\/strong><\/p>\n<p><strong>Work with a partner. The area model represents the multiplication of two fractions. Copy and complete the statement.<\/strong><\/p>\n<p>Question 1.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27040\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-4.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 4\" width=\"280\" height=\"173\" \/><\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-47970\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-1.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-1\" width=\"278\" height=\"173\" \/><br \/>\n\\(\\frac{2}{3}\\) X \\(\\frac{3}{4}\\) = \\(\\frac{6}{12}\\)<\/p>\n<p>Explanation:<br \/>\nStep I: We multiply the numerators as 2 X 3 = 6<br \/>\nStep II: We multiply the denominators as 3 X 4 =12<br \/>\nStep III: We write the fraction in the simplest form as<br \/>\n\\(\\frac{6}{12}\\),<br \/>\nSo \\(\\frac{2}{3}\\) X \\(\\frac{3}{4}\\) = \\(\\frac{6}{12}\\)<\/p>\n<p>Question 2.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27041\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-5.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 5\" width=\"285\" height=\"173\" \/><\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-47984\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-2.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-2\" width=\"278\" height=\"173\" \/><br \/>\n\\(\\frac{1}{2}\\) X \\(\\frac{2}{3}\\) = \\(\\frac{2}{6}\\)<\/p>\n<p>Explanation:<br \/>\nFirst part is \\(\\frac{1}{2}\\) and second part is \\(\\frac{2}{3}\\)<br \/>\nStep I: We multiply the numerators as 1 X 2 = 2<br \/>\nStep II: We multiply the denominators as 2 X 3 = 6<br \/>\nStep III: We write the fraction in the simplest form as<br \/>\n\\(\\frac{2}{6}\\),<br \/>\nSo \\(\\frac{1}{2}\\) X \\(\\frac{2}{3}\\) = \\(\\frac{2}{6}\\)<\/p>\n<p>Question 3.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27042\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-6.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 6\" width=\"283\" height=\"175\" \/><\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-48165\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-3-1.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-3\" width=\"280\" height=\"175\" \/><br \/>\n\\(\\frac{2}{5}\\) X \\(\\frac{2}{3}\\) = \\(\\frac{4}{15}\\)<\/p>\n<p>Explanation:<br \/>\nFirst part is \\(\\frac{2}{5}\\) and second part is \\(\\frac{2}{3}\\)<br \/>\nStep I: We multiply the numerators as 2 X 2 = 4<br \/>\nStep II: We multiply the denominators as 5 X 3 = 15<br \/>\nStep III: We write the fraction in the simplest form as<br \/>\n\\(\\frac{4}{15}\\),<br \/>\nSo \\(\\frac{2}{5}\\) X \\(\\frac{2}{3}\\) = \\(\\frac{4}{15}\\)<\/p>\n<p>Question 4.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27043\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-7.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 7\" width=\"283\" height=\"175\" \/><\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-48166\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-4.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-4\" width=\"283\" height=\"175\" \/><br \/>\n\\(\\frac{3}{4}\\) X \\(\\frac{1}{4}\\) = \\(\\frac{3}{16}\\)<\/p>\n<p>Explanation:<br \/>\nFirst part is \\(\\frac{3}{4}\\) and second part is \\(\\frac{1}{4}\\)<br \/>\nStep I: We multiply the numerators as 3 X 1 = 3<br \/>\nStep II: We multiply the denominators as 4 X 4 = 16<br \/>\nStep III: We write the fraction in the simplest form as \\(\\frac{3}{16}\\),<br \/>\nSo \\(\\frac{3}{4}\\) X \\(\\frac{1}{4}\\) = \\(\\frac{3}{16}\\)<\/p>\n<p><strong>Work with a partner. Use an area model to \ufb01nd the product.<\/strong><\/p>\n<p>Question 5.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27044\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-8.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 8\" width=\"68\" height=\"49\" \/><\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-48478\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-5-1.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-5\" width=\"268\" height=\"167\" \/><br \/>\nSo \\(\\frac{1}{2}\\) X \\(\\frac{1}{3}\\) = \\(\\frac{1}{6}\\)<\/p>\n<p>Explanation:<br \/>\nWe draw an area model to find the product<br \/>\nStep 1: We are given with \\(\\frac{1}{2}\\) so<br \/>\nwe take shade 1 part out of 2 ,<br \/>\nStep 2: We have \\(\\frac{1}{3}\\) now we shade<br \/>\n1 part out of 3<br \/>\nStep 4 : We multiply the numerators as 1 X 1 = 1<br \/>\nStep 5: We multiply the denominators as 2 X 3 = 6<br \/>\nStep 6 : The purple area came through overlapping which is the product as<br \/>\n1 part out of 6 and write the fraction<br \/>\nin the simplest form as \\(\\frac{1}{6}\\).<br \/>\nSo \\(\\frac{1}{2}\\) X \\(\\frac{1}{3}\\) = \\(\\frac{1}{6}\\)<\/p>\n<p>Question 6.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27045\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-9.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 9\" width=\"57\" height=\"44\" \/><\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-48476\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-6.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-6\" width=\"314\" height=\"167\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-6.bmp 314w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-6-300x160.jpg 300w\" sizes=\"(max-width: 314px) 100vw, 314px\" \/><\/p>\n<p>So \\(\\frac{4}{5}\\) X \\(\\frac{1}{4}\\) = \\(\\frac{4}{20}\\)<\/p>\n<p>Explanation:<br \/>\nWe draw an area model to find the product<br \/>\nStep 1: We are given with \\(\\frac{4}{5}\\) so<br \/>\nwe take shade 4 parts out of 5 ,<br \/>\nStep 2: We have \\(\\frac{1}{4}\\) now we shade<br \/>\n1 part out of 4<br \/>\nStep 4 : We multiply the numerators as 4 X 1 = 4<br \/>\nStep 5: We multiply the denominators as 5 X 4 = 20<br \/>\nStep 6 : The purple area came through overlapping which is the product as<br \/>\n4 parts out of 20 and write the fraction<br \/>\nin the simplest form as \\(\\frac{4}{20}\\).<br \/>\nSo \\(\\frac{4}{5}\\) X \\(\\frac{1}{4}\\) = \\(\\frac{4}{20}\\).<\/p>\n<p>Question 7.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27046\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-10.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 10\" width=\"66\" height=\"55\" \/><\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-48628\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-7.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-7\" width=\"314\" height=\"158\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-7.bmp 314w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-7-300x151.jpg 300w\" sizes=\"(max-width: 314px) 100vw, 314px\" \/><br \/>\nSo \\(\\frac{1}{6}\\) X \\(\\frac{3}{4}\\) = \\(\\frac{3}{24}\\)<\/p>\n<p>Explanation:<br \/>\nWe draw an area model to find the product<br \/>\nStep 1: We are given with \\(\\frac{1}{6}\\) so<br \/>\nwe take shade 1 part out of 6 ,<br \/>\nStep 2: We have \\(\\frac{3}{4}\\) now we shade<br \/>\n3 parts out of 4<br \/>\nStep 4 : We multiply the numerators as 1 X 3 = 3<br \/>\nStep 5: We multiply the denominators as 6 X 4 = 24<br \/>\nStep 6 : The purple area came through overlapping which is the product as<br \/>\n3 parts out of 24 and write the fraction<br \/>\nin the simplest form as \\(\\frac{3}{24}\\).<br \/>\nSo \\(\\frac{1}{6}\\) X \\(\\frac{3}{4}\\) = \\(\\frac{3}{24}\\).<\/p>\n<p>Question 8.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27047\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-11.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 11\" width=\"53\" height=\"41\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-48631\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-8.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-8\" width=\"314\" height=\"158\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-8.bmp 314w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-8-300x151.jpg 300w\" sizes=\"(max-width: 314px) 100vw, 314px\" \/><\/p>\n<p>So \\(\\frac{3}{5}\\) X \\(\\frac{1}{4}\\) = \\(\\frac{3}{20}\\)<\/p>\n<p>Explanation:<br \/>\nWe draw an area model to find the product<br \/>\nStep 1: We are given with \\(\\frac{3}{5}\\) so<br \/>\nwe take shade 3 parts out of 5 ,<br \/>\nStep 2: We have \\(\\frac{1}{4}\\) now we shade<br \/>\n1 part out of 4<br \/>\nStep 4 : We multiply the numerators as 3 X 1 = 3<br \/>\nStep 5: We multiply the denominators as 5 X 4 = 20<br \/>\nStep 6 : The purple area came through overlapping which is the product as<br \/>\n3 parts out of 20 and write the fraction<br \/>\nin the simplest form as \\(\\frac{3}{20}\\).<br \/>\nSo \\(\\frac{3}{5}\\) X \\(\\frac{1}{4}\\) = \\(\\frac{3}{20}\\).<\/p>\n<p>Question 9.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nYou have a recipe that serves 6 people. The recipe uses three-fourths of a cup of milk.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27048\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-12.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 12\" width=\"230\" height=\"197\" \/><br \/>\na. How can you use the recipe to serve more people? How much milk would you need? Give 2 examples.<br \/>\nb. How can you use the recipe to serve fewer people? How much milk would you need? Give 2 examples.<br \/>\na. Example 1: To serve 8 people we need<br \/>\n\\(\\frac{8}{6}\\) recipe + \\(\\frac{24}{4}\\) milk<br \/>\nExample 2 : To serve 10 people we need<br \/>\n\\(\\frac{10}{6}\\) recipe + \\(\\frac{30}{4}\\) milk.<br \/>\nb. Example 1: To serve 5 people we need<br \/>\n\\(\\frac{5}{6}\\) recipe + \\(\\frac{15}{4}\\) milk<br \/>\nExample 2 : To serve 4 people we need<br \/>\n\\(\\frac{4}{6}\\) recipe + \\(\\frac{12}{4}\\) milk.<\/p>\n<p>Explanation:<br \/>\nGiven 1 recipe serves 6 people and uses three-fourths of a cup of milk,<br \/>\na. We can use the recipe to serve more people and milk would we need are<br \/>\n6 persons = 1 recipe + \\(\\frac{3}{4}\\) milk<br \/>\n1 person = \\(\\frac{1}{6}\\) recipe + \\(\\frac{3}{4}\\) milk<br \/>\nExample 1 : 8 persons = \\(\\frac{8}{6}\\) recipe + \\(\\frac{24}{4}\\) milk<br \/>\nExample 2 : 10 persons = \\(\\frac{10}{6}\\) recipe + \\(\\frac{30}{4}\\) milk<\/p>\n<p>b. We can use the recipe to serve fewer people and milk would we need are<br \/>\n6 persons = 1 recipe + \\(\\frac{3}{4}\\) milk<br \/>\n1 person = \\(\\frac{1}{6}\\) recipe + \\(\\frac{3}{4}\\) milk<br \/>\n5 persons = \\(\\frac{5}{6}\\) recipe + \\(\\frac{15}{4}\\) milk<br \/>\n4 persons = \\(\\frac{4}{6}\\) recipe + \\(\\frac{12}{4}\\) milk.<\/p>\n<p><strong>Vocabulary<\/strong><\/p>\n<p>The following vocabulary terms are de\ufb01ned in this chapter. Think about what each term might mean and record your thoughts.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27049\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-13.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 13\" width=\"456\" height=\"40\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-13.png 456w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-13-300x26.png 300w\" sizes=\"(max-width: 456px) 100vw, 456px\" \/><br \/>\nReciprocals : In mathematics, the reciprocal, also known as multiplicative inverse,<br \/>\nis the inverse of a number x. denoted as 1\/x or x<sup>-1<\/sup>.<br \/>\nThis means that the product of a number x and its reciprocal yields 1.<br \/>\nThe reciprocal of a number is simply the number that has been flipped or<br \/>\ninverted upside-down.\u00a0This entails transposing a number such that<br \/>\nthe numerator and denominator are placed at the bottom and top respectively.<br \/>\nTo find the reciprocal of a whole number, just convert it into a fraction in<br \/>\nwhich the original number is the denominator and the numerator is 1.<br \/>\nThe reciprocal of 2\/3 is 3\/2.<br \/>\nThe product of 2\/3 and its reciprocal 3\/2 is 1.<br \/>\n2\/3 x 3\/2 = 1.<\/p>\n<h3><a id=\"Lesson_2.1_Multiplying_Fractions\"><\/a>Lesson 2.1 Multiplying Fractions<\/h3>\n<p><strong>EXPLORATION 1<\/strong><br \/>\n<strong>Using Models to Solve a Problem<\/strong><br \/>\n<strong>Work with a partner. A bottle of water is \\(\\frac{1}{2}\\) full. You drink \\(\\frac{2}{3}\\) of the water. Use one of the models to \ufb01nd the portion of the bottle of water that you drink. Explain your steps.<\/strong><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27050\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-14.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 14\" width=\"463\" height=\"429\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-14.png 463w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-14-300x278.png 300w\" sizes=\"(max-width: 463px) 100vw, 463px\" \/><\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-48651\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-9.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-9\" width=\"404\" height=\"158\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-9.bmp 404w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-9-300x117.jpg 300w\" sizes=\"(max-width: 404px) 100vw, 404px\" \/><\/p>\n<p>We use area model to give the portion of the bottle of water<br \/>\nthat I drink is \\(\\frac{1}{3}\\) of the bottle.<\/p>\n<p>Explanation:<br \/>\nGiven a bottle of water is \\(\\frac{1}{2}\\) full.<br \/>\nI drink \\(\\frac{2}{3}\\) of the water. So the portion of the bottle of water<br \/>\nthat I drink is \\(\\frac{1}{2}\\) X \\(\\frac{2}{3}\\) = \\(\\frac{2}{6}\\) =<br \/>\n\\(\\frac{1}{3}\\) of the bottle.<br \/>\nWe draw an area model to find the product<br \/>\nStep 1: We are given with \\(\\frac{1}{2}\\) so<br \/>\nwe take shade 1 part out of 2,<br \/>\nStep 2: We have \\(\\frac{2}{3}\\) now we shade<br \/>\n2 parts out of 3<br \/>\nStep 4 : We multiply the numerators as 1 X 2 = 2<br \/>\nStep 5: We multiply the denominators as 2 X 3 = 6<br \/>\nStep 6 : The purple area came through overlapping which is the product as<br \/>\n2 parts out of 6 or 1 part out of 3 and write the fraction<br \/>\nin the simplest form as \\(\\frac{2}{6}\\) or \\(\\frac{1}{3}\\)<br \/>\nSo the portion of the bottle of water that I drink is<br \/>\n\\(\\frac{2}{6}\\) = \\(\\frac{1}{3}\\) of the bottle.<\/p>\n<p><strong>EXPLORATION 2<\/strong><br \/>\n<strong>Work with a partner. A park has a playground that is \\(\\frac{3}{4}\\) of its width and \\(\\frac{4}{5}\\) of its length.<\/strong><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27051\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-15.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 15\" width=\"205\" height=\"205\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-15.png 205w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-15-150x150.png 150w\" sizes=\"(max-width: 205px) 100vw, 205px\" \/><br \/>\na. Use a model to \ufb01nd the portion of the park that is covered by the playground. Explain your steps.<br \/>\nb. How can you \ufb01nd the solution of part(a) without using a model?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27052\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-16.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 16\" width=\"159\" height=\"175\" \/><br \/>\na.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-48654\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-10.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-10\" width=\"347\" height=\"161\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-10.bmp 347w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-10-300x139.jpg 300w\" sizes=\"(max-width: 347px) 100vw, 347px\" \/><br \/>\nThe portion of the park that is covered by the playground is<br \/>\n\\(\\frac{12}{20}\\) = \\(\\frac{3}{5}\\)<\/p>\n<p>b. Without using a model the portion of the park that is covered by the playground is \\(\\frac{12}{20}\\) = \\(\\frac{3}{5}\\).<\/p>\n<p>Explanation:<br \/>\na. Used area model to \ufb01nd the portion of the park that is covered by the playground.<br \/>\nGiven a\u00a0park has a playground that is \\(\\frac{3}{4}\\) of its width and<br \/>\n\\(\\frac{4}{5}\\) of its length. So the portion of the park<br \/>\nthat is covered by the playground is \\(\\frac{3}{4}\\) X \\(\\frac{4}{5}\\)<br \/>\nwe explain this by an area model as<br \/>\nStep 1: We are given with \\(\\frac{3}{4}\\) so we take shade 3 parts out of 4,<br \/>\nStep 2: We have \\(\\frac{4}{5}\\) now we shade 4 parts out of 5<br \/>\nStep 4 : We multiply the numerators as 3 X 4 = 12<br \/>\nStep 5: We multiply the denominators as 4 X 5 = 20<br \/>\nStep 6 : The purple area came through overlapping which is the product as<br \/>\n12 parts out of 20 or 3 part out of 5 and write the fraction<br \/>\nin the simplest form as \\(\\frac{12}{20}\\) or \\(\\frac{3}{5}\\)<br \/>\nThe portion of the park that is covered by the playground is<br \/>\n\\(\\frac{12}{20}\\) = \\(\\frac{3}{5}\\).<\/p>\n<p>b. Without using a model we have first part is \\(\\frac{3}{4}\\) and<br \/>\nsecond part is \\(\\frac{4}{5}\\)<br \/>\nStep I: We multiply the numerators as 3 X 4 = 12<br \/>\nStep II: We multiply the denominators as 4 X 5 = 20<br \/>\nStep III: We write the fraction in the simplest form as<br \/>\n\\(\\frac{12}{20}\\) or \\(\\frac{3}{5}\\),<br \/>\nThe portion of the park that is covered by the playground is \\(\\frac{12}{20}\\) =<br \/>\n\\(\\frac{3}{5}\\).<\/p>\n<p><strong>2.1 Lesson<\/strong><\/p>\n<p><strong>Try It<\/strong><br \/>\n<strong>Multiply.<\/strong><\/p>\n<p>Question 1.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27053\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-17.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 17\" width=\"59\" height=\"46\" \/><\/p>\n<p>\\(\\frac{1}{3}\\) X \\(\\frac{1}{5}\\) = \\(\\frac{1}{15}\\)<\/p>\n<p>Explanation:<br \/>\nStep I: We multiply the numerators as 1 X 1 = 1<br \/>\nStep II: We multiply the denominators as 3 X 5 =15<br \/>\nStep III: We write the fraction in the simplest form as<br \/>\n\\(\\frac{1}{15}\\),<br \/>\nSo \\(\\frac{1}{3}\\) X \\(\\frac{1}{5}\\) = \\(\\frac{1}{15}\\).<\/p>\n<p>Question 2.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27054\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-18.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 18\" width=\"55\" height=\"56\" \/><br \/>\n\\(\\frac{2}{3}\\) X \\(\\frac{3}{4}\\) = \\(\\frac{6}{12}\\)<br \/>\n= \\(\\frac{2}{4}\\) = \\(\\frac{1}{2}\\)<\/p>\n<p>Explanation:<br \/>\nStep I: We multiply the numerators as 2 X 3 = 6<br \/>\nStep II: We multiply the denominators as 3 X 4 =12<br \/>\nStep III: We write the fraction in the simplest form as \\(\\frac{6}{12}\\),<br \/>\nSo \\(\\frac{2}{3}\\) X \\(\\frac{3}{4}\\) = \\(\\frac{6}{12}\\)=<br \/>\n= \\(\\frac{2}{4}\\) as both can go in 2 we get latex]\\frac{1}{2}[\/latex].<\/p>\n<p>Question 3.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27055\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-19.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 19\" width=\"56\" height=\"53\" \/><br \/>\nSo \\(\\frac{1}{2}\\) X \\(\\frac{5}{6}\\) = \\(\\frac{5}{12}\\)<\/p>\n<p>Explanation:<br \/>\nStep I: We multiply the numerators as 1 X 5 = 5<br \/>\nStep II: We multiply the denominators as 2 X 6 =12<br \/>\nStep III: We write the fraction in the simplest form as \\(\\frac{5}{12}\\),<br \/>\nSo \\(\\frac{1}{2}\\) X \\(\\frac{5}{6}\\) = \\(\\frac{5}{12}\\).<\/p>\n<p><strong>Key Idea<\/strong><br \/>\n<strong>Multiplying Fractions<\/strong><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27056\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-20.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 20\" width=\"275\" height=\"111\" \/><\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Multiply. Write the answer in simplest form.<\/strong><\/p>\n<p>Question 4.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27057\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-21.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 21\" width=\"60\" height=\"47\" \/><\/p>\n<p>\\(\\frac{3}{7}\\) X \\(\\frac{2}{3}\\) = \\(\\frac{6}{21}\\) = \\(\\frac{2}{7}\\)<\/p>\n<p>Explanation:<br \/>\nStep I: We multiply the numerators as 3 X 2 = 6<br \/>\nStep II: We multiply the denominators as 7 X 3 =21<br \/>\nStep III: We write the fraction in the simplest form as \\(\\frac{6}{21}\\),<br \/>\nSo \\(\\frac{3}{7}\\) X \\(\\frac{2}{3}\\) = \\(\\frac{6}{21}\\) =<br \/>\nfurther simplified as both go in 3 we get \\(\\frac{2}{7}\\).<\/p>\n<p>Question 5.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27058\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-22.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 22\" width=\"56\" height=\"54\" \/><br \/>\n\\(\\frac{4}{9}\\) X \\(\\frac{3}{10}\\) = \\(\\frac{12}{90}\\) =<br \/>\n\\(\\frac{2}{15}\\)<\/p>\n<p>Explanation:<br \/>\nStep I: We multiply the numerators as 4 X 3 = 12<br \/>\nStep II: We multiply the denominators as 9 X 10 =90<br \/>\nStep III: We write the fraction in the simplest form as \\(\\frac{12}{90}\\),<br \/>\nSo \\(\\frac{4}{9}\\) X \\(\\frac{3}{10}\\) = \\(\\frac{12}{90}\\)<br \/>\nfurther can be simplified as both can be divided by 6 we get 2 X 6 = 12 and<br \/>\n15 x 6 = 90, (2, 15) So \\(\\frac{12}{90}\\) = \\(\\frac{2}{15}\\).<\/p>\n<p>Question 6.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27059\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-23.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 23\" width=\"53\" height=\"50\" \/><br \/>\n\\(\\frac{6}{5}\\) X \\(\\frac{5}{8}\\) = \\(\\frac{30}{40}\\) =\\(\\frac{3}{4}\\)<\/p>\n<p>Explanation:<br \/>\nStep I: We multiply the numerators as 6 X 5 = 30<br \/>\nStep II: We multiply the denominators as 5 X 8 =40<br \/>\nStep III: We write the fraction in the simplest form as \\(\\frac{30}{40}\\),<br \/>\nSo \\(\\frac{6}{5}\\) X \\(\\frac{5}{8}\\) = \\(\\frac{30}{40}\\)<br \/>\nfurther can be simplified as both can be divided by 10 we get 3 X 10 = 30 and<br \/>\n4 x 10 = 40,(3,4) So \\(\\frac{30}{40}\\) = \\(\\frac{3}{4}\\).<\/p>\n<p><strong>Try It<\/strong><\/p>\n<p>Question 7.<br \/>\n<strong>WHAT IF?<\/strong><br \/>\nYou use \\(\\frac{1}{4}\\) of the \ufb02our to make the dough.<br \/>\nHow much of the entire bag do you use to make the dough?<\/p>\n<p>\\(\\frac{1}{4}\\) of the entire bag we do use to make the dough<\/p>\n<p>Explanation:<br \/>\nGiven we use \\(\\frac{1}{4}\\) of the flour to make the dough,<br \/>\nWe take entire bag as 1 which has flour , So we use<br \/>\n\\(\\frac{1}{4}\\) out of 1 means \\(\\frac{1}{4}\\) X 1 = \\(\\frac{1}{4}\\)<br \/>\nof the entire bag we do use to make the dough.<\/p>\n<p>Key Idea<br \/>\nMultiplying Mixed Numbers<br \/>\nWrite each mixed number as an improper fraction. Then multiply as you would with fractions.<\/p>\n<p><strong>Try It<\/strong><br \/>\n<strong>Multiply. Write the answer in simplest form.<\/strong><\/p>\n<p>Question 8.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27060\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-24.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 24\" width=\"68\" height=\"53\" \/><br \/>\n\\(\\frac{1}{3}\\) X \\(\\frac{7}{6}\\) = \\(\\frac{7}{18}\\)<\/p>\n<p>Explanation:<br \/>\nGiven \\(\\frac{1}{3}\\) X 1 \\(\\frac{1}{6}\\) so<br \/>\nfirst we write mixed number 1 \\(\\frac{1}{6}\\)\u00a0 as 1 X 6 + 1 by 6 = \\(\\frac{7}{6}\\) now<br \/>\nwe multiply \\(\\frac{1}{3}\\)\u00a0 X \u00a0\\(\\frac{7}{6}\\),<br \/>\nStep I: We multiply the numerators as 1 X 7 = 7<br \/>\nStep II: We multiply the denominators as 3 X 6 =18<br \/>\nStep III: We write the fraction in the simplest form as \\(\\frac{7}{18}\\),<br \/>\nSo \\(\\frac{1}{3}\\) X \\(\\frac{7}{6}\\) = \\(\\frac{7}{18}\\).<\/p>\n<p>Question 9.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27061\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-25.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 25\" width=\"64\" height=\"46\" \/><br \/>\n\\(\\frac{7}{2}\\) X \\(\\frac{4}{9}\\) = \\(\\frac{28}{18}\\) = \\(\\frac{14}{9}\\) = 1 \\(\\frac{5}{9}\\)<\/p>\n<p>Explanation:<br \/>\nGiven 3 \\(\\frac{1}{2}\\) X \\(\\frac{4}{9}\\) so<br \/>\nfirst we write mixed number 3 \\(\\frac{1}{2}\\) as 3 X 2 + 1 by 2 = \\(\\frac{7}{2}\\) now we multiply \\(\\frac{7}{2}\\)\u00a0 X \u00a0\\(\\frac{4}{9}\\),<br \/>\nStep I: We multiply the numerators as 7 X 4 = 28<br \/>\nStep II: We multiply the denominators as 2 X 9 =18<br \/>\nStep III: We write the fraction in the simplest form as \\(\\frac{28}{18}\\),<br \/>\nwe can further simplify as both goes in 2, 14 X 2 = 28 and 9 X 2 = 18, (14,9)<br \/>\nSo 3 \\(\\frac{1}{2}\\) X \\(\\frac{4}{9}\\) = \\(\\frac{28}{18}\\)\u00a0 = \\(\\frac{14}{9}\\). As numerator is greater than denominator we write in mixed fraction also as (1 X 9 + 5 by 9 ), 1\\(\\frac{5}{9}\\).<\/p>\n<p>Question 10.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27062\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-26.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 26\" width=\"64\" height=\"50\" \/><br \/>\n4 \\(\\frac{2}{3}\\) X \\(\\frac{3}{4}\\) = \\(\\frac{42}{12}\\)\u00a0 = \\(\\frac{7}{2}\\) = 3 \\(\\frac{1}{2}\\).<\/p>\n<p>Explanation:<br \/>\nGiven 4 \\(\\frac{2}{3}\\) X \\(\\frac{3}{4}\\) so<br \/>\nfirst we write mixed number 4 \\(\\frac{2}{3}\\) as 4 X 3 + 2 by 3 = \\(\\frac{14}{3}\\) now we multiply \\(\\frac{14}{3}\\)\u00a0 X \u00a0\\(\\frac{3}{4}\\),<br \/>\nStep I: We multiply the numerators as 14 X 3 = 42<br \/>\nStep II: We multiply the denominators as 3 X 4 =12<br \/>\nStep III: We write the fraction in the simplest form as \\(\\frac{42}{12}\\),<br \/>\nwe can further simplify as both goes in 6, 6 X 7 = 42 and 6 X 2 = 12, (7,2)<br \/>\nSo 4 \\(\\frac{2}{3}\\) X \\(\\frac{3}{4}\\) = \\(\\frac{42}{12}\\)\u00a0 = \\(\\frac{7}{2}\\). As numerator is greater than denominator we write in<br \/>\nmixed fraction also as (3 X 2 + 1 by 2 ), 3 \\(\\frac{1}{2}\\).<\/p>\n<p><strong>Try It<br \/>\nMultiply. Write the answer in simplest form.<\/strong><\/p>\n<p>Question 11.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27063\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-27.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 27\" width=\"76\" height=\"45\" \/><br \/>\n1 \\(\\frac{7}{8}\\) X 2 \\(\\frac{2}{5}\\) = \\(\\frac{180}{40}\\) = \\(\\frac{9}{2}\\) = 4 \\(\\frac{1}{2}\\).<\/p>\n<p>Explanation :<br \/>\n1 \\(\\frac{7}{8}\\) X 2 \\(\\frac{2}{5}\\) , We write mixed fractions<br \/>\n1 \\(\\frac{7}{8}\\) as 1 X 8 + 7 by 8 = \\(\\frac{15}{8}\\) and 2 \\(\\frac{2}{5}\\) as 2 X 5 + 2 by 5 = \\(\\frac{12}{5}\\) Now we multiply<br \/>\n\\(\\frac{15}{8}\\) X \\(\\frac{12}{5}\\),<br \/>\nStep I: We multiply the numerators as 15 X 12 = 180<br \/>\nStep II: We multiply the denominators as 8 X 5 =40<br \/>\nStep III: We write the fraction in the simplest form as \\(\\frac{180}{40}\\),<br \/>\nwe can further simplify as both goes in 20, 20 X 9 = 180 and 20 X 2 = 40, (9,2),<br \/>\n1 \\(\\frac{7}{8}\\) X 2 \\(\\frac{2}{5}\\) = \\(\\frac{180}{40}\\) = \\(\\frac{9}{2}\\) , As numerator is greater than denominator we write in<br \/>\nmixed fraction also as (4 X 2 + 1 by 2 ), 4 \\(\\frac{1}{2}\\).<\/p>\n<p>Question 12.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27064\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-28.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 28\" width=\"87\" height=\"51\" \/><br \/>\n5 \\(\\frac{5}{7}\\) X 2 \\(\\frac{1}{10}\\) = \\(\\frac{840}{70}\\) = 12<\/p>\n<p>Explanation :<br \/>\n5 \\(\\frac{5}{7}\\) X 2 \\(\\frac{1}{10}\\) , We write mixed fractions<br \/>\n5 \\(\\frac{5}{7}\\) as 5 X 7 + 5 by 7 = \\(\\frac{40}{7}\\) and 2 \\(\\frac{1}{10}\\) as 2 X 10 + 1 by 10 = \\(\\frac{21}{10}\\) Now we multiply<br \/>\n\\(\\frac{40}{7}\\) X \\(\\frac{21}{10}\\),<br \/>\nStep I: We multiply the numerators as 40 X 21 = 840<br \/>\nStep II: We multiply the denominators as 7 X 10 =70<br \/>\nStep III: We write the fraction in the simplest form as \\(\\frac{840}{70}\\),<br \/>\nwe can further simplify as both goes in 70, 70 X 12 = 840 and 70 X 1 = 70, (12,1), therefore<br \/>\n5 \\(\\frac{5}{7}\\) X 2 \\(\\frac{1}{10}\\) = \\(\\frac{840}{70}\\) = 12 .<\/p>\n<p>Question 13.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27065\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-29.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 29\" width=\"69\" height=\"51\" \/><br \/>\n2 \\(\\frac{1}{3}\\) X 7 \\(\\frac{2}{3}\\) = \\(\\frac{161}{9}\\) = 17 \\(\\frac{8}{9}\\)<\/p>\n<p>Explanation:<br \/>\n2 \\(\\frac{1}{3}\\) X 7 \\(\\frac{2}{3}\\) , We write mixed fractions<br \/>\n2 \\(\\frac{1}{3}\\) as 2 X 3 + 1 by 3 = \\(\\frac{7}{3}\\) and 7 \\(\\frac{2}{3}\\) as 7 X 3 + 2 by 3 = \\(\\frac{23}{3}\\) Now we multiply<br \/>\n\\(\\frac{7}{3}\\) X \\(\\frac{23}{3}\\),<br \/>\nStep I: We multiply the numerators as 7 X 23 = 161<br \/>\nStep II: We multiply the denominators as 3 X 3 =9<br \/>\nStep III: We write the fraction in the simplest form as \\(\\frac{161}{9}\\),<br \/>\ntherefore 2 \\(\\frac{1}{3}\\) X 7 \\(\\frac{2}{3}\\) = \\(\\frac{161}{9}\\),<br \/>\nAs numerator is greater than denominator we write in<br \/>\nmixed fraction also as (17 X 9 + 8 by 9 ), 17 \\(\\frac{8}{9}\\).<\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><\/p>\n<p>Solve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p><strong>MULTIPLYING FRACTIONS AND MIXED NUMBERS<\/strong><br \/>\n<strong>Multiply. Write the answer in simplest form.<\/strong><\/p>\n<p>Question 14.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27066\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-30.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 30\" width=\"59\" height=\"47\" \/><br \/>\n\\(\\frac{1}{8}\\) X \\(\\frac{1}{6}\\) = \\(\\frac{1}{48}\\)<\/p>\n<p>Explanation:<br \/>\nStep I: We multiply the numerators as 1 X 1 = 1<br \/>\nStep II: We multiply the denominators as 8 X 6 =48<br \/>\nStep III: We write the fraction in the simplest form as \\(\\frac{1}{48}\\),<br \/>\nSo \\(\\frac{1}{8}\\) X \\(\\frac{1}{6}\\) = \\(\\frac{1}{48}\\).<\/p>\n<p>Question 15.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27067\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-31.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 31\" width=\"56\" height=\"50\" \/><\/p>\n<p>\\(\\frac{3}{8}\\) X \\(\\frac{2}{3}\\) = \\(\\frac{6}{24}\\) = \\(\\frac{1}{4}\\)<\/p>\n<p>Explanation:<br \/>\nStep I: We multiply the numerators as 3 X 2 = 6<br \/>\nStep II: We multiply the denominators as 8 X 3 =24<br \/>\nStep III: We write the fraction in the simplest form as \\(\\frac{6}{24}\\),<br \/>\nwe can further simplify as both goes in 6, 6 X 1 = 6 and 6 X 4 = 24, (1,4),<br \/>\nSo \\(\\frac{3}{8}\\) X \\(\\frac{2}{3}\\) = \\(\\frac{6}{24}\\) = \\(\\frac{1}{4}\\).<\/p>\n<p>Question 16.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27068\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-32.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 32\" width=\"76\" height=\"50\" \/><\/p>\n<p>2 \\(\\frac{1}{6}\\) X 4 \\(\\frac{2}{5}\\) = \\(\\frac{286}{30}\\) = \\(\\frac{143}{15}\\) = 9 \\(\\frac{8}{15}\\)<\/p>\n<p>Explanation:<br \/>\n2 \\(\\frac{1}{6}\\) X 4 \\(\\frac{2}{5}\\) , We write mixed fractions<br \/>\n2 \\(\\frac{1}{6}\\) as 2 X 6 + 1 by 6 = \\(\\frac{13}{6}\\) and 4 \\(\\frac{2}{5}\\) as 4 X 5 + 2 by 5 = \\(\\frac{22}{5}\\) Now we multiply<br \/>\n\\(\\frac{13}{6}\\) X \\(\\frac{22}{5}\\),<br \/>\nStep I: We multiply the numerators as 13 X 22 = 286<br \/>\nStep II: We multiply the denominators as 6 X 5 =30<br \/>\nStep III: We write the fraction in the simplest form as \\(\\frac{286}{30}\\),<br \/>\nwe can further simplify as both goes in 2, 2 X 143 = 286 and 2 X 15 = 30, (143,15),<br \/>\ntherefore 2 \\(\\frac{1}{6}\\) X 4 \\(\\frac{2}{5}\\) = \\(\\frac{286}{30}\\) =<br \/>\n\\(\\frac{143}{15}\\). As numerator is greater than denominator we write in<br \/>\nmixed fraction also as (9 X 15 + 8 by 15 ), 9 \\(\\frac{8}{15}\\).<\/p>\n<p>Question 17.<br \/>\n<strong>REASONING<\/strong><br \/>\nWhat is the missing denominator?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27069\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-33.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 33\" width=\"119\" height=\"67\" \/><br \/>\nThe missing denominator is 4<\/p>\n<p>Explanation:<br \/>\nLet us take the missing denominator as x now we have<br \/>\ndenominators as 7 X x = 28, so x = \\(\\frac{28}{7}\\) = 4.<\/p>\n<p>Question 18.<br \/>\n<strong>USING TOOLS<\/strong><br \/>\nWrite a multiplication problem involving fractions that is represented by the model. Explain your reasoning.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27070\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-34.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 34\" width=\"170\" height=\"108\" \/><\/p>\n<p>The multiplication problem involving fractions that is represented by the model<br \/>\n\\(\\frac{4}{5}\\) X \\(\\frac{1}{3}\\) = \\(\\frac{4}{15}\\)<\/p>\n<p>Explanation:<br \/>\nGiven the area model as shown in figure we take the first fraction part<br \/>\nas 4 out of 5 as yellow area represents 4 parts out of 5 and the second fraction<br \/>\npart is 1 out of 3 with blue now the products of fraction is<br \/>\n\\(\\frac{4}{5}\\) X \\(\\frac{1}{3}\\) =<br \/>\nStep I: We multiply the numerators as 4 X 1 = 4<br \/>\nStep II: We multiply the denominators as 5 X 3 = 15<br \/>\nStep III: We write the fraction in the simplest form as \\(\\frac{4}{15}\\),<br \/>\nwhich is the green area came through overlapping which is the product as<br \/>\n4 parts out of 15, Therefore the multiplication problem involving fractions<br \/>\nthat is represented by the model is \\(\\frac{4}{5}\\) X \\(\\frac{1}{3}\\) = \\(\\frac{4}{15}\\).<\/p>\n<p>Question 19.<br \/>\n<strong>USING TOOLS<\/strong><br \/>\nUse the number line to \ufb01nd <img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27072\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-35.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 35\" width=\"45\" height=\"45\" \/> Explain your reasoning.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27071\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-35.1.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 35.1\" width=\"355\" height=\"57\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-35.1.png 355w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-35.1-300x48.png 300w\" sizes=\"(max-width: 355px) 100vw, 355px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-49327\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-11.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-11\" width=\"349\" height=\"156\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-11.bmp 349w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-11-300x134.jpg 300w\" sizes=\"(max-width: 349px) 100vw, 349px\" \/><br \/>\n\\(\\frac{3}{4}\\) X \\(\\frac{1}{2}\\) = \\(\\frac{3}{8}\\)<\/p>\n<p>Explanation:<br \/>\nWe write 1\/2 as 4 by 8 on the number line,<br \/>\nnow we take 3 parts of 4 from 4\/8 we get results as<br \/>\n\\(\\frac{3}{8}\\) on the number line or we take 3 times \\(\\frac{1}{8}\\) on<br \/>\nnumber line we get \\(\\frac{3}{8}\\).<br \/>\nTherefore \\(\\frac{3}{4}\\) X \\(\\frac{1}{2}\\) = \\(\\frac{3}{8}\\).<\/p>\n<p><strong>Self-Assessment for Problem Solving<\/strong><\/p>\n<p>Solve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 20.<br \/>\nYou spend \\(\\frac{5}{12}\\) of a day at an amusement park. You spend \\(\\frac{2}{5}\\) of that time riding waterslides. How many hours do you spend riding waterslides? Draw a model to show why your answer makes sense.<br \/>\nI spent 4 hours for riding waterslides<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-49395\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-11-3.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-11\" width=\"1469\" height=\"508\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-11-3.bmp 1469w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-11-3-300x104.jpg 300w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-11-3-1024x354.jpg 1024w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-11-3-768x266.jpg 768w\" sizes=\"(max-width: 1469px) 100vw, 1469px\" \/><\/p>\n<p>Explanation:<br \/>\nGiven I spend \\(\\frac{5}{12}\\) of a day at an amusement park means<br \/>\nout of 24 hours so hours spent at the park is \\(\\frac{5}{12}\\) X 24 = 10 hours.<br \/>\nNow in 10 hours we spend \\(\\frac{2}{5}\\) of that time riding waterslides means<br \/>\nnumber of hours spent riding waterslides is 10 X \\(\\frac{2}{5}\\) = 4 hours.<br \/>\nSo I spent 4 hours for riding waterslides.<br \/>\nWe take area model as shown in the picture first part as 5 out of 12 and second part as 24<br \/>\nwe get 120 by 12 as 10 hours and from 10 hours we spent 2 out of 5 we get 4 hours.<\/p>\n<p>Question 21.<br \/>\nA venue is preparing for a concert on the \ufb02oor shown. The width of the red carpet is \\(\\frac{1}{6}\\) of the width of the \ufb02oor. What is the area of the red carpet?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27074\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-36.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 36\" width=\"171\" height=\"209\" \/><br \/>\nThe area of the red carpet is 1057 square feet<\/p>\n<p>Explanation:<br \/>\nGiven the width of floor is 63 feet, So width of the red carpet is \\(\\frac{1}{6}\\) X 63 =<br \/>\n\\(\\frac{63}{6}\\) we can simplify as both goes in 3we get \\(\\frac{21}{2}\\),<br \/>\nNow we write length of floor 100 \\(\\frac{2}{3}\\) as 100 X 3 + 2 by 3 as \\(\\frac{302}{3}\\), Now we has width and length of the carpet so area of the carpet is<br \/>\n\\(\\frac{302}{3}\\) X \\(\\frac{21}{2}\\) = \\(\\frac{6342}{6}\\)<br \/>\nboth goes in 6 so we get 1057 square feet.<\/p>\n<p>Question 22.<br \/>\nYou travel 9\\(\\frac{3}{8}\\) miles from your house to a shopping mall. You travel \\(\\frac{2}{3}\\) of that distance on an interstate. The only road construction you encounter is on the \ufb01rst \\(\\frac{2}{5}\\) of the interstate. On how many miles of your trip do you encounter construction?<\/p>\n<p>I encounter \\(\\frac{5}{2}\\) or 2\u00a0\\(\\frac{1}{2}\\) miles of construction of my trip.<\/p>\n<p>Explanation:<br \/>\nGiven I travel 9\\(\\frac{3}{8}\\) we write mixed fraction as fraction as<br \/>\n9 X 8 + 3 by 8 = \\(\\frac{75}{8}\\) now I travel \\(\\frac{2}{3}\\) of that distance on an interstate,<br \/>\nSo the distance on the interstate is \\(\\frac{2}{3}\\)\u00a0 X \\(\\frac{75}{8}\\) = \\(\\frac{150}{24}\\) both goes in 6 we get \\(\\frac{25}{4}\\) miles.<br \/>\nNow in \\(\\frac{25}{4}\\) the only construction I encounter is \\(\\frac{2}{5}\\) of<br \/>\n\\(\\frac{25}{4}\\),<br \/>\nSo \\(\\frac{2}{5}\\) X \\(\\frac{25}{4}\\) =<br \/>\n\\(\\frac{50}{20}\\) = \\(\\frac{5}{2}\\) miles,<br \/>\nAs numerator is greater than denominator we write in mixed fraction<br \/>\nalso as (2 X 2 + 1 by 2 ), 2 \\(\\frac{1}{2}\\) miles.<\/p>\n<h3><a id=\"Multiplying_Fractions_Homework_&amp;_Practice_2.1\"><\/a>Multiplying Fractions Homework &amp; Practice 2.1<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Find the LCM of the numbers.<\/strong><\/p>\n<p>Question 1.<br \/>\n8, 10<br \/>\nThe LCM of 8, 10 is 40<\/p>\n<p>Explanation:<br \/>\nThe\u00a0<span class=\"GlossaryTerm\">LCM<\/span>\u00a0is the smallest\u00a0<span class=\"GlossaryTerm\">positive number<\/span>\u00a0that all of the numbers\u00a0<span class=\"GlossaryTerm\">divide<\/span>\u00a0into evenly.<br \/>\nOne way is to list the multiples of each number, then choose the common multiples,<br \/>\nthen the least one.<br \/>\nMultiples of<span id=\"MathJax-Element-2-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-6\" class=\"mjx-math\"><span id=\"MJXc-Node-7\" class=\"mjx-mrow\"><span id=\"MJXc-Node-8\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-9\" class=\"mjx-mrow\"><span id=\"MJXc-Node-10\" class=\"mjx-mrow\"><span id=\"MJXc-Node-11\" class=\"mjx-mspace\"><\/span><span id=\"MJXc-Node-12\" class=\"mjx-mtext\"> <\/span><span id=\"MJXc-Node-13\" class=\"mjx-mspace\"><\/span><\/span><span id=\"MJXc-Node-14\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\">8<\/span><\/span><span id=\"MJXc-Node-15\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">:<\/span><\/span><span id=\"MJXc-Node-16\" class=\"mjx-mrow\"><span id=\"MJXc-Node-17\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">{<\/span><\/span><span id=\"MJXc-Node-18\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\">8<\/span><\/span><span id=\"MJXc-Node-19\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">,<\/span><\/span><span id=\"MJXc-Node-20\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\">16<\/span><\/span><span id=\"MJXc-Node-21\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">,<\/span><\/span><span id=\"MJXc-Node-22\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\">24<\/span><\/span><span id=\"MJXc-Node-23\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">,<\/span><\/span><span id=\"MJXc-Node-24\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\">32<\/span><\/span><span id=\"MJXc-Node-25\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">,<\/span><\/span><span id=\"MJXc-Node-26\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-27\" class=\"mjx-mrow\"><span id=\"MJXc-Node-28\" class=\"mjx-mrow\"><span id=\"MJXc-Node-29\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\">40<\/span><\/span><\/span><\/span><\/span><span id=\"MJXc-Node-30\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">,<\/span><\/span><span id=\"MJXc-Node-31\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\">48<\/span><\/span><span id=\"MJXc-Node-32\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">,<\/span><\/span><span id=\"MJXc-Node-33\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\">56<\/span><\/span><span id=\"MJXc-Node-34\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">,<\/span><\/span><span id=\"MJXc-Node-35\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\">64<\/span><\/span><span id=\"MJXc-Node-36\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">,<\/span><\/span><span id=\"MJXc-Node-37\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\">72<\/span><\/span><span id=\"MJXc-Node-38\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">,<\/span><\/span><span id=\"MJXc-Node-39\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-40\" class=\"mjx-mrow\"><span id=\"MJXc-Node-41\" class=\"mjx-mrow\"><span id=\"MJXc-Node-42\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\">80<\/span><\/span><\/span><\/span><\/span><span id=\"MJXc-Node-43\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">,<\/span><\/span><span id=\"MJXc-Node-44\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">&#8230;<\/span><\/span><span id=\"MJXc-Node-45\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">}<br \/>\n<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>Multiples of<span id=\"MathJax-Element-3-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-46\" class=\"mjx-math\"><span id=\"MJXc-Node-47\" class=\"mjx-mrow\"><span id=\"MJXc-Node-48\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-49\" class=\"mjx-mrow\"><span id=\"MJXc-Node-50\" class=\"mjx-mrow\"><span id=\"MJXc-Node-51\" class=\"mjx-mspace\"><\/span><span id=\"MJXc-Node-52\" class=\"mjx-mtext\"> <\/span><span id=\"MJXc-Node-53\" class=\"mjx-mspace\"><\/span><\/span><span id=\"MJXc-Node-54\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\">10<\/span><\/span><span id=\"MJXc-Node-55\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">:<\/span><\/span><span id=\"MJXc-Node-56\" class=\"mjx-mrow\"><span id=\"MJXc-Node-57\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">{<\/span><\/span><span id=\"MJXc-Node-58\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\">10<\/span><\/span><span id=\"MJXc-Node-59\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">,<\/span><\/span><span id=\"MJXc-Node-60\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\">20<\/span><\/span><span id=\"MJXc-Node-61\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">,<\/span><\/span><span id=\"MJXc-Node-62\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\">30<\/span><\/span><span id=\"MJXc-Node-63\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">,<\/span><\/span><span id=\"MJXc-Node-64\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-65\" class=\"mjx-mrow\"><span id=\"MJXc-Node-66\" class=\"mjx-mrow\"><span id=\"MJXc-Node-67\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\">40<\/span><\/span><\/span><\/span><\/span><span id=\"MJXc-Node-68\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">,<\/span><\/span><span id=\"MJXc-Node-69\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\">50<\/span><\/span><span id=\"MJXc-Node-70\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">,<\/span><\/span><span id=\"MJXc-Node-71\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\">60<\/span><\/span><span id=\"MJXc-Node-72\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">,<\/span><\/span><span id=\"MJXc-Node-73\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\">70<\/span><\/span><span id=\"MJXc-Node-74\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">,<\/span><\/span><span id=\"MJXc-Node-75\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-76\" class=\"mjx-mrow\"><span id=\"MJXc-Node-77\" class=\"mjx-mrow\"><span id=\"MJXc-Node-78\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\">80<\/span><\/span><\/span><\/span><\/span><span id=\"MJXc-Node-79\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">,<\/span><\/span><span id=\"MJXc-Node-80\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\">90<\/span><\/span><span id=\"MJXc-Node-81\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">,<\/span><\/span><span id=\"MJXc-Node-82\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">&#8230;<\/span><\/span><span id=\"MJXc-Node-83\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">}<br \/>\n<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>Common Multiples are<span id=\"MathJax-Element-4-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-84\" class=\"mjx-math\"><span id=\"MJXc-Node-85\" class=\"mjx-mrow\"><span id=\"MJXc-Node-86\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-87\" class=\"mjx-mrow\"><span id=\"MJXc-Node-88\" class=\"mjx-mrow\"><span id=\"MJXc-Node-89\" class=\"mjx-mspace\"><\/span><span id=\"MJXc-Node-90\" class=\"mjx-mtext\"> <\/span><span id=\"MJXc-Node-91\" class=\"mjx-mspace\"><\/span><\/span><span id=\"MJXc-Node-92\" class=\"mjx-mrow\"><span id=\"MJXc-Node-93\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">{<\/span><\/span><span id=\"MJXc-Node-94\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-95\" class=\"mjx-mrow\"><span id=\"MJXc-Node-96\" class=\"mjx-mrow\"><span id=\"MJXc-Node-97\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\">40<\/span><\/span><span id=\"MJXc-Node-98\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">,<\/span><\/span><span id=\"MJXc-Node-99\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\">80<\/span><\/span><span id=\"MJXc-Node-100\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">,<\/span><\/span><span id=\"MJXc-Node-101\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">.<\/span><\/span><span id=\"MJXc-Node-102\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">.<\/span><\/span><\/span><\/span><\/span><span id=\"MJXc-Node-103\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">}<br \/>\n<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span id=\"MathJax-Element-5-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-104\" class=\"mjx-math\"><span id=\"MJXc-Node-105\" class=\"mjx-mrow\"><span id=\"MJXc-Node-106\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-107\" class=\"mjx-mrow\"><span id=\"MJXc-Node-108\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\">therefore L<\/span><\/span><span id=\"MJXc-Node-109\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\">C<\/span><\/span><span id=\"MJXc-Node-110\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\">M<\/span><\/span><span id=\"MJXc-Node-111\" class=\"mjx-mrow\"><span id=\"MJXc-Node-112\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">(<\/span><\/span><span id=\"MJXc-Node-113\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\">8<\/span><\/span><span id=\"MJXc-Node-114\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">,<\/span><\/span><span id=\"MJXc-Node-115\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\">10<\/span><\/span><span id=\"MJXc-Node-116\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">)<\/span><\/span><\/span><span id=\"MJXc-Node-117\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">=<\/span><\/span><span id=\"MJXc-Node-118\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\">40.<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>Question 2.<br \/>\n5, 7<br \/>\nThe LCM of 5, 7 is 35<\/p>\n<p>Explanation:<br \/>\nThe\u00a0<span class=\"GlossaryTerm\">LCM<\/span>\u00a0is the smallest\u00a0<span class=\"GlossaryTerm\">positive number<\/span>\u00a0that all of the numbers\u00a0<span class=\"GlossaryTerm\">divide<\/span>\u00a0into evenly.<br \/>\nOne way is to list the multiples of each number, then choose the common multiples,<br \/>\nthen the least one.<br \/>\nMultiples of<span id=\"MathJax-Element-2-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-6\" class=\"mjx-math\"><span id=\"MJXc-Node-7\" class=\"mjx-mrow\"><span id=\"MJXc-Node-8\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-9\" class=\"mjx-mrow\"><span id=\"MJXc-Node-10\" class=\"mjx-mrow\"><span id=\"MJXc-Node-11\" class=\"mjx-mspace\"><\/span><span id=\"MJXc-Node-12\" class=\"mjx-mtext\"> 5<\/span><\/span><span id=\"MJXc-Node-15\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">:<\/span><\/span><span id=\"MJXc-Node-16\" class=\"mjx-mrow\"><span id=\"MJXc-Node-17\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">{5<\/span><\/span><span id=\"MJXc-Node-19\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">,<\/span><\/span><span id=\"MJXc-Node-20\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\">10<\/span><\/span><span id=\"MJXc-Node-21\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">,15<\/span><\/span><span id=\"MJXc-Node-23\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">,<\/span><\/span><span id=\"MJXc-Node-24\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\">20<\/span><\/span><span id=\"MJXc-Node-25\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">,25<\/span><\/span><span id=\"MJXc-Node-30\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">,30<\/span><\/span><span id=\"MJXc-Node-32\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">,35<\/span><\/span><span id=\"MJXc-Node-34\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">,40<\/span><\/span><span id=\"MJXc-Node-36\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">,45<\/span><\/span><span id=\"MJXc-Node-38\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">,50<\/span><\/span><span id=\"MJXc-Node-43\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">,<\/span><\/span><span id=\"MJXc-Node-44\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">&#8230;<\/span><\/span><span id=\"MJXc-Node-45\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">}<br \/>\n<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>Multiples of<span id=\"MathJax-Element-3-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-46\" class=\"mjx-math\"><span id=\"MJXc-Node-47\" class=\"mjx-mrow\"><span id=\"MJXc-Node-48\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-49\" class=\"mjx-mrow\"><span id=\"MJXc-Node-50\" class=\"mjx-mrow\"><span id=\"MJXc-Node-51\" class=\"mjx-mspace\"><\/span><span id=\"MJXc-Node-52\" class=\"mjx-mtext\"> 7<\/span><\/span><span id=\"MJXc-Node-55\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">:<\/span><\/span><span id=\"MJXc-Node-56\" class=\"mjx-mrow\"><span id=\"MJXc-Node-57\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">{7<\/span><\/span><span id=\"MJXc-Node-59\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">,14<\/span><\/span><span id=\"MJXc-Node-61\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">,21<\/span><\/span><span id=\"MJXc-Node-68\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">,28<\/span><\/span><span id=\"MJXc-Node-70\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">,35<\/span><\/span><span id=\"MJXc-Node-72\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">,42<\/span><\/span><span id=\"MJXc-Node-74\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">,49<\/span><\/span><span id=\"MJXc-Node-79\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">,56<\/span><\/span><span id=\"MJXc-Node-81\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">,<\/span><\/span><span id=\"MJXc-Node-82\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">&#8230;<\/span><\/span><span id=\"MJXc-Node-83\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">}<br \/>\n<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>Common Multiples\u00a0<span id=\"MathJax-Element-4-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-84\" class=\"mjx-math\"><span id=\"MJXc-Node-85\" class=\"mjx-mrow\"><span id=\"MJXc-Node-86\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-87\" class=\"mjx-mrow\"><span id=\"MJXc-Node-88\" class=\"mjx-mrow\"><span id=\"MJXc-Node-89\" class=\"mjx-mspace\"><\/span><span id=\"MJXc-Node-90\" class=\"mjx-mtext\"> <\/span><span id=\"MJXc-Node-91\" class=\"mjx-mspace\"><\/span><\/span><span id=\"MJXc-Node-92\" class=\"mjx-mrow\"><span id=\"MJXc-Node-93\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">{35<\/span><\/span><span id=\"MJXc-Node-94\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-95\" class=\"mjx-mrow\"><span id=\"MJXc-Node-96\" class=\"mjx-mrow\"><span id=\"MJXc-Node-100\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">,<\/span><\/span><span id=\"MJXc-Node-101\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">.<\/span><\/span><span id=\"MJXc-Node-102\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">.<\/span><\/span><\/span><\/span><\/span><span id=\"MJXc-Node-103\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">}<br \/>\n<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span id=\"MathJax-Element-5-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-104\" class=\"mjx-math\"><span id=\"MJXc-Node-105\" class=\"mjx-mrow\"><span id=\"MJXc-Node-106\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-107\" class=\"mjx-mrow\"><span id=\"MJXc-Node-108\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\">therefore L<\/span><\/span><span id=\"MJXc-Node-109\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\">C<\/span><\/span><span id=\"MJXc-Node-110\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\">M<\/span><\/span><span id=\"MJXc-Node-111\" class=\"mjx-mrow\"><span id=\"MJXc-Node-112\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">(5<\/span><\/span><span id=\"MJXc-Node-114\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">,7<\/span><\/span><span id=\"MJXc-Node-116\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">)<\/span><\/span><\/span><span id=\"MJXc-Node-117\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">=35<\/span><\/span><span id=\"MJXc-Node-118\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\">.<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>Question 3.<br \/>\n2, 5, 7<br \/>\nThe LCM of 2,5,7 is 70<\/p>\n<p>Explanation:<br \/>\nThe\u00a0<span class=\"GlossaryTerm\">LCM<\/span>\u00a0is the smallest\u00a0<span class=\"GlossaryTerm\">positive number<\/span>\u00a0that all of the numbers\u00a0<span class=\"GlossaryTerm\">divide<\/span> into evenly.<br \/>\n<span style=\"font-size: 16px;\">1. List the <\/span><span class=\"GlossaryTerm\" style=\"font-size: 16px;\">prime<\/span><span style=\"font-size: 16px;\">\u00a0<\/span><span class=\"GlossaryTerm\" style=\"font-size: 16px;\">factors<\/span><span style=\"font-size: 16px;\"> of each number.<br \/>\n<\/span><span style=\"font-size: 16px;\">2. <\/span><span class=\"GlossaryTerm\" style=\"font-size: 16px;\">Multiply<\/span><span style=\"font-size: 16px;\">\u00a0each\u00a0<\/span><span class=\"GlossaryTerm\" style=\"font-size: 16px;\">factor<\/span><span style=\"font-size: 16px;\"> the greatest number of times it occurs in either number.<br \/>\n<\/span><span style=\"font-size: 16px;\">Since <\/span><span style=\"font-size: 18.08px;\">2 <\/span><span style=\"font-size: 16px;\">has no\u00a0<\/span><span class=\"GlossaryTerm\" style=\"font-size: 16px;\">factors<\/span><span style=\"font-size: 16px;\">\u00a0besides\u00a0<\/span><span id=\"MathJax-Element-5-Frame\" class=\"mjx-chtml MathJax_CHTML\" style=\"line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 18.08px; letter-spacing: normal; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px;\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mstyle displaystyle=&quot;true&quot;&gt;&lt;mn&gt;1&lt;\/mn&gt;&lt;\/mstyle&gt;&lt;\/math&gt;\"><span id=\"MJXc-Node-21\" class=\"mjx-math\" aria-hidden=\"true\"><span id=\"MJXc-Node-22\" class=\"mjx-mrow\"><span id=\"MJXc-Node-23\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-24\" class=\"mjx-mrow\"><span id=\"MJXc-Node-25\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\">1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span style=\"font-size: 16px;\"> and 2,<\/span><span style=\"font-size: 16px;\"><br \/>\n<\/span><span style=\"font-size: 16px;\">2 is a <\/span><span class=\"GlossaryTerm\" style=\"font-size: 16px;\">prime<\/span><span style=\"font-size: 16px;\"> number,<br \/>\n<\/span><span style=\"font-size: 16px;\">Since\u00a0<\/span><span id=\"MathJax-Element-8-Frame\" class=\"mjx-chtml MathJax_CHTML\" style=\"line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 18.08px; letter-spacing: normal; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px;\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mstyle displaystyle=&quot;true&quot;&gt;&lt;mn&gt;7&lt;\/mn&gt;&lt;\/mstyle&gt;&lt;\/math&gt;\"><span id=\"MJXc-Node-36\" class=\"mjx-math\" aria-hidden=\"true\"><span id=\"MJXc-Node-37\" class=\"mjx-mrow\"><span id=\"MJXc-Node-38\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-39\" class=\"mjx-mrow\"><span id=\"MJXc-Node-40\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\">7<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span style=\"font-size: 16px;\">\u00a0has no\u00a0<\/span><span class=\"GlossaryTerm\" style=\"font-size: 16px;\">factors<\/span><span style=\"font-size: 16px;\"> besides <\/span><span style=\"font-size: 18.08px;\">1 and 7.<br \/>\n<\/span><span style=\"font-size: 16px;\">7 is a <\/span><span class=\"GlossaryTerm\" style=\"font-size: 16px;\">prime<\/span><span style=\"font-size: 16px;\"> number,<br \/>\n<\/span><span style=\"font-size: 16px;\">Since <\/span><span style=\"font-size: 18.08px;\">5<\/span><span style=\"font-size: 16px;\">\u00a0has no\u00a0<\/span><span class=\"GlossaryTerm\" style=\"font-size: 16px;\">factors<\/span><span style=\"font-size: 16px;\"> besides 1 and 5.<br \/>\n<\/span><span style=\"font-size: 16px;\">5 is a <\/span><span class=\"GlossaryTerm\" style=\"font-size: 16px;\">prime<\/span><span style=\"font-size: 16px;\"> number,<br \/>\n<\/span><span style=\"font-size: 16px;\">The\u00a0<\/span><span class=\"GlossaryTerm\" style=\"font-size: 16px;\">LCM<\/span><span style=\"font-size: 16px;\"> of <\/span><span style=\"font-size: 18.08px;\">2,5,7<\/span><span style=\"font-size: 16px;\">\u00a0is the result of multiplying all\u00a0<\/span><span class=\"GlossaryTerm\" style=\"font-size: 16px;\">prime<\/span><span style=\"font-size: 16px;\">\u00a0<\/span><span class=\"GlossaryTerm\" style=\"font-size: 16px;\">factors<br \/>\n<\/span><span style=\"font-size: 16px;\">the greatest number of times they occur in either number<\/span><span style=\"font-size: 18.08px;\"> 2 X 5 X 7 = 70,<br \/>\nSo the LCM of 2,5,7 is 70.<\/span><\/p>\n<p>Question 4.<br \/>\n6, 7, 10<br \/>\nThe LCM of 6, 7, 10 is 210<\/p>\n<p>Explanation:<br \/>\nCommon division of 6 ,7, 10 is<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-49425\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-12.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-12\" width=\"157\" height=\"104\" \/><\/p>\n<p>\u2234 So the LCM of the given numbers is 2 X 5 X 3 X 7 = 210.<\/p>\n<p><strong>Divide. Use a diagram to justify your answer.<\/strong><\/p>\n<p>Question 5.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27073\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-36.1.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 36.1\" width=\"56\" height=\"47\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27073\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-36.1.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 36.1\" width=\"56\" height=\"47\" \/>= 6 X 2 = 12<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-49427\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-13.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-13\" width=\"215\" height=\"104\" \/><br \/>\nExplanation:<br \/>\nGiven 6 divides \\(\\frac{5}{2}\\)\u00a0 we get 6 X 2 = 12,<br \/>\nwe take 6 parts in that we are dividing by \\(\\frac{1}{2}\\) we<br \/>\nare getting 12 parts of a whole.<\/p>\n<p>Question 6.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27075\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-37.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 37\" width=\"52\" height=\"43\" \/><br \/>\n<img decoding=\"async\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-37.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 37\" \/>= 8 X 4 = 32<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-49434\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-14.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-14\" width=\"404\" height=\"104\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-14.bmp 404w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-14-300x77.jpg 300w\" sizes=\"(max-width: 404px) 100vw, 404px\" \/><br \/>\nExplanation:<br \/>\nGiven 8 divides \\(\\frac{1}{4}\\)\u00a0 we get 8 X 4 = 32,<br \/>\nwe take 8 parts in that we are dividing by \\(\\frac{1}{4}\\) we<br \/>\nare getting 32 parts of a whole.<\/p>\n<p>Question 7.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27076\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-38.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 38\" width=\"59\" height=\"62\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27076\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-38.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 38\" width=\"59\" height=\"62\" \/>= 12<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-49436\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-15.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-15\" width=\"263\" height=\"104\" \/><br \/>\nExplanation:<br \/>\nGiven 4 divides \\(\\frac{1}{3}\\)\u00a0 we get 4 X 3 = 12,<br \/>\nwe take 4 parts in that we are dividing by \\(\\frac{1}{3}\\) we<br \/>\nare getting 12 parts of a whole.<\/p>\n<p>Question 8.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27077\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-39.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 39\" width=\"56\" height=\"61\" \/><br \/>\n<img decoding=\"async\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-39.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 39\" \/>= 4 X 5 = 20<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-49442\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-16-1.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-16\" width=\"347\" height=\"108\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-16-1.bmp 347w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-16-1-300x93.jpg 300w\" sizes=\"(max-width: 347px) 100vw, 347px\" \/><br \/>\nExplanation:<br \/>\nGiven 4 divides \\(\\frac{1}{5}\\)\u00a0 we get 4 X 5 = 20,<br \/>\nwe take 4 parts in that we are dividing by \\(\\frac{1}{5}\\) we<br \/>\nare getting 20 parts of a whole.<\/p>\n<p><strong>Write the product as a power.<\/strong><\/p>\n<p>Question 9.<br \/>\n10 \u00d7 10 \u00d7 10<\/p>\n<p>10 X 10 X 10 =10<sup>3<\/sup><\/p>\n<p>Explanation:<br \/>\nGiven expression as 10 X 10 X 10 as 10 is multiplied by 3 times we write it as<br \/>\npower of 10 as 10<sup>3<\/sup>.<\/p>\n<p>Question 10.<br \/>\n5 \u00d7 5 \u00d7 5 \u00d7 5<\/p>\n<p>5 \u00d7 5 \u00d7 5 \u00d7 5 = 5<sup>4<\/sup><\/p>\n<p>Explanation:<br \/>\nGiven expression as 5 X 5 X 5 X 5 as 5 is multiplied by 4 times we write it as<br \/>\npower of 5 as 5<sup>4<\/sup>.<\/p>\n<p>Question 11.<br \/>\nHow many inches are in 5\\(\\frac{1}{2}\\) yards?<br \/>\nA. 15\\(\\frac{1}{2}\\)<br \/>\nB. 16\\(\\frac{1}{2}\\)<br \/>\nC. 66<br \/>\nD. 198<\/p>\n<p>D, 5\\(\\frac{1}{2}\\) yards = 198<\/p>\n<p>Explanation:<br \/>\nGiven 5\\(\\frac{1}{2}\\) yards first we write mixed fractions into<br \/>\nfractions as 5 X 2 + 1 by 2 as \\(\\frac{11}{2}\\) yards as we know 1 yard is equal to<br \/>\n36 inches so \\(\\frac{11}{2}\\) = \\(\\frac{11}{2}\\)\u00a0 X 36 = \\(\\frac{396}{2}\\) = 198 , So it matches with D bit.<\/p>\n<p><strong>Concepts, Skills, &amp; Problem Solving<\/strong><br \/>\n<strong>CHOOSE TOOLS A bottle of water is \\(\\frac{2}{3}\\) full. You drink the given portion of the water. Use a model to \ufb01nd the portion of the bottle of water that you drink.<\/strong> (See Exploration 1, p. 45.)<\/p>\n<p>Question 12.<br \/>\n\\(\\frac{1}{2}\\)<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-49506\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-17.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-17\" width=\"392\" height=\"164\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-17.bmp 392w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-17-300x126.jpg 300w\" sizes=\"(max-width: 392px) 100vw, 392px\" \/><\/p>\n<p>We use area model to give the portion of the bottle of water<br \/>\nthat I drink is \\(\\frac{1}{3}\\) of the bottle.<\/p>\n<p>Explanation:<br \/>\nGiven a bottle of water is \\(\\frac{2}{3}\\) full.<br \/>\nI drink \\(\\frac{1}{2}\\) of the water. So the portion of the bottle of water<br \/>\nthat I drink is \\(\\frac{2}{3}\\) X \\(\\frac{1}{2}\\) = \\(\\frac{2}{6}\\) =<br \/>\n\\(\\frac{1}{3}\\) of the bottle.<br \/>\nWe draw an area model to find the product<br \/>\nStep 1: We are given with \\(\\frac{2}{3}\\) so<br \/>\nwe take shade 2 part out of 3,<br \/>\nStep 2: We have \\(\\frac{1}{2}\\) now we shade<br \/>\n1 part out of 2<br \/>\nStep 4 : We multiply the numerators as 2 X 1 = 2<br \/>\nStep 5: We multiply the denominators as 3 X 2 = 6<br \/>\nStep 6 : The purple area came through overlapping which is the product as<br \/>\n2 parts out of 6 or 1 part out of 3 and write the fraction<br \/>\nin the simplest form as \\(\\frac{2}{6}\\) or \\(\\frac{1}{3}\\)<br \/>\nSo the portion of the bottle of water that I drink is \\(\\frac{2}{6}\\) =<br \/>\n\\(\\frac{1}{3}\\) of the bottle.<\/p>\n<p>Question 13.<br \/>\n\\(\\frac{1}{4}\\)<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-49507\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-18.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-18\" width=\"390\" height=\"164\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-18.bmp 390w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-18-300x126.jpg 300w\" sizes=\"(max-width: 390px) 100vw, 390px\" \/><\/p>\n<p>We use area model to give the portion of the bottle of water<br \/>\nthat I drink is \\(\\frac{1}{6}\\) of the bottle.<\/p>\n<p>Explanation:<br \/>\nGiven a bottle of water is \\(\\frac{2}{3}\\) full.<br \/>\nI drink \\(\\frac{1}{4}\\) of the water. So the portion of the bottle of water<br \/>\nthat I drink is \\(\\frac{2}{3}\\) X \\(\\frac{1}{4}\\) = \\(\\frac{2}{12}\\) =<br \/>\n\\(\\frac{1}{6}\\) of the bottle.<br \/>\nWe draw an area model to find the product<br \/>\nStep 1: We are given with \\(\\frac{2}{3}\\) so<br \/>\nwe take shade 2 part out of 3,<br \/>\nStep 2: We have \\(\\frac{1}{4}\\) now we shade<br \/>\n1 part out of 4<br \/>\nStep 4 : We multiply the numerators as 2 X 1 = 2<br \/>\nStep 5: We multiply the denominators as 3 X 4 = 12<br \/>\nStep 6 : The purple area came through overlapping which is the product as<br \/>\n2 parts out of 12 or 1 part out of 6 and write the fraction<br \/>\nin the simplest form as \\(\\frac{2}{12}\\) or \\(\\frac{1}{6}\\)<br \/>\nSo the portion of the bottle of water that I drink is \\(\\frac{2}{12}\\) =<br \/>\n\\(\\frac{1}{6}\\) of the bottle.<\/p>\n<p>Question 14.<br \/>\n\\(\\frac{3}{4}\\)<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-49511\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-19.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-19\" width=\"391\" height=\"164\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-19.bmp 391w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-19-300x126.jpg 300w\" sizes=\"(max-width: 391px) 100vw, 391px\" \/><\/p>\n<p>We use area model to give the portion of the bottle of water<br \/>\nthat I drink is \\(\\frac{1}{2}\\) of the bottle.<\/p>\n<p>Explanation:<br \/>\nGiven a bottle of water is \\(\\frac{2}{3}\\) full.<br \/>\nI drink \\(\\frac{3}{4}\\) of the water. So the portion of the bottle of water<br \/>\nthat I drink is \\(\\frac{2}{3}\\) X \\(\\frac{3}{4}\\) = \\(\\frac{6}{12}\\) =<br \/>\n\\(\\frac{1}{2}\\) of the bottle.<br \/>\nWe draw an area model to find the product<br \/>\nStep 1: We are given with \\(\\frac{2}{3}\\) so<br \/>\nwe take shade 2 part out of 3,<br \/>\nStep 2: We have \\(\\frac{3}{4}\\) now we shade<br \/>\n3 parts out of 4<br \/>\nStep 4 : We multiply the numerators as 2 X 3 = 6<br \/>\nStep 5: We multiply the denominators as 3 X 4 = 12<br \/>\nStep 6 : The purple area came through overlapping which is the product as<br \/>\n6 parts out of 12 or 1 part out of 2 and write the fraction<br \/>\nin the simplest form as \\(\\frac{6}{12}\\) or \\(\\frac{1}{2}\\)<br \/>\nSo the portion of the bottle of water that I drink is \\(\\frac{6}{12}\\) =<br \/>\n\\(\\frac{1}{2}\\) of the bottle.<\/p>\n<p><strong>MULTIPLYING FRACTIONS<\/strong><br \/>\n<strong>Multiply. Write the answer in simplest form.<\/strong><\/p>\n<p>Question 15.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27078\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-40.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 40\" width=\"64\" height=\"47\" \/><br \/>\n<img decoding=\"async\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-40.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 40\" \/>= \\(\\frac{2}{21}\\)<\/p>\n<p>\\(\\frac{1}{7}\\) X \\(\\frac{2}{3}\\) = \\(\\frac{2}{21}\\)<\/p>\n<p>Explanation:<br \/>\nGiven expression as \\(\\frac{1}{7}\\) X \\(\\frac{2}{3}\\)<br \/>\nStep I: We multiply the numerators as 1 X 2 = 2<br \/>\nStep II: We multiply the denominators as 7 X 3 = 21<br \/>\nStep III: We write the fraction in the simplest form as \\(\\frac{2}{21}\\),<br \/>\nSo \\(\\frac{1}{7}\\) X \\(\\frac{2}{3}\\) = \\(\\frac{2}{21}\\).<\/p>\n<p>Question 16.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27079\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-41.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 41\" width=\"46\" height=\"49\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27079\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-41.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 41\" width=\"46\" height=\"49\" \/>= \\(\\frac{5}{16}\\)<\/p>\n<p>\\(\\frac{5}{8}\\) X \\(\\frac{1}{2}\\) = \\(\\frac{5}{16}\\)<\/p>\n<p>Explanation:<br \/>\nGiven expression as \\(\\frac{5}{8}\\) X \\(\\frac{1}{2}\\)<br \/>\nStep I: We multiply the numerators as 5 X 1 = 5<br \/>\nStep II: We multiply the denominators as 8 X 2 = 16<br \/>\nStep III: We write the fraction in the simplest form as \\(\\frac{5}{16}\\),<br \/>\nSo \\(\\frac{5}{8}\\) X \\(\\frac{1}{2}\\) = \\(\\frac{5}{16}\\).<\/p>\n<p>Question 17.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27080\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-42.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 42\" width=\"56\" height=\"44\" \/><br \/>\n<img decoding=\"async\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-42.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 42\" \/>= \\(\\frac{1}{10}\\)<\/p>\n<p>\\(\\frac{1}{4}\\) X \\(\\frac{2}{5}\\) = \\(\\frac{2}{20}\\) = \\(\\frac{1}{10}\\)<\/p>\n<p>Explanation:<br \/>\nGiven expression as \\(\\frac{1}{4}\\) X \\(\\frac{2}{5}\\)<br \/>\nStep I: We multiply the numerators as 1 X 2 = 2<br \/>\nStep II: We multiply the denominators as 4 X 5 = 20<br \/>\nStep III: We write the fraction in the simplest form as \\(\\frac{2}{20}\\),<br \/>\nwe can further simplify as both goes in 2, 2 X 1 = 2 and 2 X 10 = 20, (1,10),<br \/>\nSo \\(\\frac{1}{4}\\) X \\(\\frac{2}{5}\\) = \\(\\frac{2}{20}\\) = \\(\\frac{1}{10}\\)<\/p>\n<p>Question 18.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27081\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-43.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 43\" width=\"52\" height=\"44\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27081\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-43.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 43\" width=\"52\" height=\"44\" \/>= \\(\\frac{3}{28}\\)<\/p>\n<p>\\(\\frac{3}{7}\\) X \\(\\frac{1}{4}\\) = \\(\\frac{3}{28}\\)<\/p>\n<p>Explanation:<br \/>\nGiven expression as \\(\\frac{3}{7}\\) X \\(\\frac{1}{4}\\)<br \/>\nStep I: We multiply the numerators as 3 X 1 = 3<br \/>\nStep II: We multiply the denominators as 7 X 4 = 28<br \/>\nStep III: We write the fraction in the simplest form as \\(\\frac{3}{28}\\),<br \/>\nSo \\(\\frac{3}{7}\\) X \\(\\frac{1}{4}\\) = \\(\\frac{3}{28}\\).<\/p>\n<p>Question 19.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27082\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-44.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 44\" width=\"56\" height=\"52\" \/><br \/>\n<img decoding=\"async\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-44.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 44\" \/>= \\(\\frac{8}{21}\\)<\/p>\n<p>\\(\\frac{2}{3}\\) X \\(\\frac{4}{7}\\) = \\(\\frac{8}{21}\\)<\/p>\n<p>Explanation:<br \/>\nGiven expression as \\(\\frac{2}{3}\\) X \\(\\frac{4}{7}\\)<br \/>\nStep I: We multiply the numerators as 3 X 1 = 3<br \/>\nStep II: We multiply the denominators as 7 X 4 = 28<br \/>\nStep III: We write the fraction in the simplest form as \\(\\frac{3}{28}\\),<br \/>\nSo \\(\\frac{2}{3}\\) X \\(\\frac{4}{7}\\) = \\(\\frac{8}{21}\\).<\/p>\n<p>Question 20.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27083\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-45.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 45\" width=\"54\" height=\"46\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27083\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-45.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 45\" width=\"54\" height=\"46\" \/> = \\(\\frac{5}{8}\\)<\/p>\n<p>\\(\\frac{5}{7}\\) X \\(\\frac{7}{8}\\) = \\(\\frac{35}{56}\\) = \\(\\frac{5}{8}\\)<\/p>\n<p>Explanation:<\/p>\n<p>Given expression as \\(\\frac{5}{7}\\) X \\(\\frac{7}{8}\\)<br \/>\nStep I: We multiply the numerators as 5 X 7 = 35<br \/>\nStep II: We multiply the denominators as 7 X 8 = 56<br \/>\nStep III: We write the fraction in the simplest form as \\(\\frac{35}{56}\\),<br \/>\nwe can further simplify as both goes in 7, 7 X 5 = 35 and 7 X 8 = 56, (5,8),<br \/>\nSo \\(\\frac{5}{7}\\) X \\(\\frac{7}{8}\\) = \\(\\frac{35}{56}\\) = \\(\\frac{5}{8}\\).<\/p>\n<p>Question 21.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27084\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-46.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 46\" width=\"50\" height=\"50\" \/><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-46.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 46\" \/>= \\(\\frac{1}{24}\\)<\/p>\n<p>\\(\\frac{3}{8}\\) X \\(\\frac{1}{9}\\) = \\(\\frac{3}{72}\\) = \\(\\frac{1}{24}\\)<\/p>\n<p>Explanation:<br \/>\nGiven expression as \\(\\frac{3}{8}\\) X \\(\\frac{1}{9}\\)<br \/>\nStep I: We multiply the numerators as 3 X 1 = 3<br \/>\nStep II: We multiply the denominators as 8 X 9 = 72<br \/>\nStep III: We write the fraction in the simplest form as \\(\\frac{3}{72}\\),<br \/>\nwe can further simplify as both goes in 3, 3 X 1 = 3 and 3 X 24 = 72, (1,24),<br \/>\nSo \\(\\frac{3}{8}\\) X \\(\\frac{1}{9}\\) = \\(\\frac{3}{72}\\) = \\(\\frac{1}{24}\\).<\/p>\n<p>Question 22.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27085\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-47.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 47\" width=\"47\" height=\"48\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27085\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-47.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 47\" width=\"47\" height=\"48\" \/>= \\(\\frac{1}{3}\\)<\/p>\n<p>\\(\\frac{5}{6}\\) X \\(\\frac{2}{5}\\) = \\(\\frac{10}{30}\\) = \\(\\frac{1}{3}\\)<\/p>\n<p>Explanation:<\/p>\n<p>Given expression as \\(\\frac{5}{6}\\) X \\(\\frac{2}{5}\\)<br \/>\nStep I: We multiply the numerators as 5 X 2 = 10<br \/>\nStep II: We multiply the denominators as 6 X 5 = 30<br \/>\nStep III: We write the fraction in the simplest form as \\(\\frac{10}{30}\\),<br \/>\nwe can further simplify as both goes in 10, 10 X 1 = 10 and 10 X 3 = 30, (1,3),<br \/>\nSo \\(\\frac{5}{6}\\) X \\(\\frac{2}{5}\\) = \\(\\frac{10}{30}\\) = \\(\\frac{1}{3}\\).<\/p>\n<p>Question 23.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27086\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-48.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 48\" width=\"67\" height=\"43\" \/><br \/>\n<img decoding=\"async\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-48.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 48\" \/>=\u00a0\\(\\frac{25}{6}\\) = 4 \\(\\frac{1}{6}\\)<\/p>\n<p>\\(\\frac{5}{12}\\) X 10 = \\(\\frac{50}{12}\\) = \\(\\frac{25}{6}\\) =<br \/>\n4 \\(\\frac{1}{6}\\)<\/p>\n<p>Explanation:<\/p>\n<p>Given expression as \\(\\frac{5}{12}\\) X 10<br \/>\nStep I: We multiply the numerators as 5 X 10 = 50<br \/>\nStep II: Denominators will be same as 12<br \/>\nStep III: We write the fraction in the simplest form as \\(\\frac{50}{12}\\),<br \/>\nwe can further simplify as both goes in 2, 2 X 25 = 50 and 2 X 6 = 12, (25,6),<br \/>\n\\(\\frac{25}{6}\\) . As numerator is greater than denominator we write in mixed fraction also as ( 4 X 6 + 1 by 6 ), 4 \\(\\frac{1}{6}\\). So \\(\\frac{5}{12}\\) X 10 = \\(\\frac{50}{12}\\) = \\(\\frac{25}{6}\\) = 4 \\(\\frac{1}{6}\\).<\/p>\n<p>Question 24.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27087\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-49.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 49\" width=\"53\" height=\"46\" \/><br \/>\n<img decoding=\"async\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-49.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 49\" \/>= \\(\\frac{21}{4}\\) = 5\\(\\frac{1}{4}\\)<\/p>\n<p>Explanation:<br \/>\nGiven expression as 6 X \\(\\frac{7}{8}\\)<br \/>\nStep I: We multiply the numerators as 6 X 7 = 42<br \/>\nStep II: Denominators will be same as 8<br \/>\nStep III: We write the fraction in the simplest form as \\(\\frac{42}{8}\\),<br \/>\nwe can further simplify as both goes in 2, 2 X 21 = 42 and 2 X 4 = 8, (21,4),<br \/>\n\\(\\frac{21}{4}\\). So 6 X \\(\\frac{7}{8}\\)\u00a0 = \\(\\frac{42}{8}\\) = \\(\\frac{21}{4}\\) as numerator is greater we write as (5 X 4 + 1 by 4), 5\\(\\frac{1}{4}\\).<\/p>\n<p>Question 25.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27088\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-50.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 50\" width=\"62\" height=\"52\" \/><br \/>\n<img decoding=\"async\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-50.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 50\" \/>=\u00a0\\(\\frac{2}{5}\\)<\/p>\n<p>\\(\\frac{3}{4}\\) X \\(\\frac{8}{15}\\) = \\(\\frac{24}{60}\\) = \\(\\frac{2}{5}\\)<\/p>\n<p>Explanation:<br \/>\nGiven expression as \\(\\frac{3}{4}\\) X \\(\\frac{8}{15}\\)<br \/>\nStep I: We multiply the numerators as 3 X 8 = 24<br \/>\nStep II: We multiply the denominators as 4 X 15 = 60<br \/>\nStep III: We write the fraction in the simplest form as \\(\\frac{24}{60}\\),<br \/>\nwe can further simplify as both goes in 12, 12 X 2 = 24 and 12 X 5 = 60, (2,5),<br \/>\nSo \\(\\frac{3}{4}\\) X \\(\\frac{8}{15}\\) = \\(\\frac{24}{60}\\) = \\(\\frac{2}{5}\\).<\/p>\n<p>Question 26.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27089\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-51.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 51\" width=\"54\" height=\"54\" \/><br \/>\n<img decoding=\"async\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-51.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 51\" \/>= \\(\\frac{16}{45}\\)<\/p>\n<p>\\(\\frac{4}{9}\\) X \\(\\frac{4}{5}\\) = \\(\\frac{16}{45}\\)<\/p>\n<p>Explanation:<\/p>\n<p>Given expression as \\(\\frac{4}{9}\\) X \\(\\frac{4}{5}\\)<br \/>\nStep I: We multiply the numerators as 4 X 4 = 16<br \/>\nStep II: We multiply the denominators as 9 X 5 = 45<br \/>\nStep III: We write the fraction in the simplest form as \\(\\frac{16}{45}\\),<br \/>\nSo \\(\\frac{4}{9}\\) X \\(\\frac{4}{5}\\) = \\(\\frac{16}{45}\\).<\/p>\n<p>Question 27.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27090\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-52.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 52\" width=\"51\" height=\"43\" \/><br \/>\n<img decoding=\"async\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-52.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 52\" \/>= \\(\\frac{9}{49}\\)<\/p>\n<p>\\(\\frac{3}{7}\\) X \\(\\frac{3}{7}\\) = \\(\\frac{9}{49}\\)<\/p>\n<p>Explanation:<br \/>\ngiven expression as \\(\\frac{3}{7}\\) X \\(\\frac{3}{7}\\)<br \/>\nStep I: We multiply the numerators as 3 X 3 = 9<br \/>\nStep II: We multiply the denominators as 7 X 7 = 49<br \/>\nStep III: We write the fraction in the simplest form as \\(\\frac{9}{49}\\),<br \/>\nSo \\(\\frac{3}{7}\\) X \\(\\frac{3}{7}\\) = \\(\\frac{9}{49}\\).<\/p>\n<p>Question 28.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27091\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-53.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 53\" width=\"60\" height=\"44\" \/><br \/>\n<img decoding=\"async\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-53.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 53\" \/>= \\(\\frac{5}{27}\\)<\/p>\n<p>\\(\\frac{5}{6}\\) X \\(\\frac{2}{9}\\) = \\(\\frac{10}{54}\\) = \\(\\frac{5}{27}\\)<\/p>\n<p>Explanation:<\/p>\n<p>given expression as \\(\\frac{5}{6}\\) X \\(\\frac{2}{9}\\)<br \/>\nStep I: We multiply the numerators as 5 X 2 = 10<br \/>\nStep II: We multiply the denominators as 6 X 9 = 54<br \/>\nStep III: We write the fraction in the simplest form as \\(\\frac{10}{54}\\),<br \/>\nwe can further simplify as both goes in 2, 2 X 5 = 10 and 2 X 27 = 54, (5,27),<br \/>\nSo \\(\\frac{5}{6}\\) X \\(\\frac{2}{9}\\) = \\(\\frac{10}{54}\\) = \\(\\frac{5}{27}\\).<\/p>\n<p>Question 29.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27092\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-54.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 54\" width=\"65\" height=\"53\" \/><br \/>\n<img decoding=\"async\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-54.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 54\" \/>= \\(\\frac{13}{21}\\)<\/p>\n<p>\\(\\frac{13}{18}\\) X \\(\\frac{6}{7}\\) = \\(\\frac{78}{126}\\) = \\(\\frac{13}{21}\\)<\/p>\n<p>Explanation:<\/p>\n<p>Given expression as \\(\\frac{13}{18}\\) X \\(\\frac{6}{7}\\)<br \/>\nStep I: We multiply the numerators as 13 X 6 = 78<br \/>\nStep II: We multiply the denominators as 18 X 7 = 126<br \/>\nStep III: We write the fraction in the simplest form as \\(\\frac{78}{126}\\),<br \/>\nwe can further simplify as both goes in 6, 6 X 13 = 78 and 6 X 21 = 126, (13,21),<br \/>\nSo \\(\\frac{13}{18}\\) X \\(\\frac{6}{7}\\) = \\(\\frac{78}{126}\\) = \\(\\frac{13}{21}\\).<\/p>\n<p>Question 30.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27093\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-55.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 55\" width=\"53\" height=\"42\" \/><br \/>\n<img decoding=\"async\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-55.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 55\" \/>= \\(\\frac{49}{30}\\) = 1 \\(\\frac{19}{30}\\)<\/p>\n<p>\\(\\frac{7}{9}\\) X \\(\\frac{21}{10}\\) = \\(\\frac{147}{90}\\) = \\(\\frac{49}{30}\\) = 1 \\(\\frac{19}{30}\\)<\/p>\n<p>Explanation:<br \/>\nGiven expression as \\(\\frac{7}{9}\\) X \\(\\frac{21}{10}\\)<br \/>\nStep I: We multiply the numerators as 7 X 21 = 147<br \/>\nStep II: We multiply the denominators as 9 X 10 = 90<br \/>\nStep III: We write the fraction in the simplest form as \\(\\frac{147}{90}\\),<br \/>\nwe can further simplify as both goes in 3, 3 X 49 = 147 and 3 X 30 = 90, (147,90),<br \/>\n<span style=\"font-size: 16px;\">\\(\\frac{49}{30}\\). As numerator is greater than denominator we write in mixed fraction also as (1 X 30 + 19 by 30 ), 1 \\(\\frac{19}{30}\\). Therefore \\(\\frac{7}{9}\\) X \\(\\frac{21}{10}\\) = \\(\\frac{147}{90}\\) = \\(\\frac{49}{30}\\) =<br \/>\n1 \\(\\frac{19}{30}\\).<\/span><\/p>\n<p>Question 31.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nIn an aquarium, \\(\\frac{2}{5}\\) of the \ufb01sh are surgeon\ufb01sh. Of these, \\(\\frac{3}{4}\\) are yellow tangs. What portion of all \ufb01sh in the aquarium are yellow tangs?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27094\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-56.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 56\" width=\"316\" height=\"288\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-56.png 316w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-56-300x273.png 300w\" sizes=\"(max-width: 316px) 100vw, 316px\" \/><br \/>\n\\(\\frac{3}{10}\\) portion of all \ufb01sh in the aquarium are yellow tangs<\/p>\n<p>Explanation:<br \/>\nGiven in an aquarium, \\(\\frac{2}{5}\\) of the \ufb01sh are surgeon\ufb01sh. Of these, \\(\\frac{3}{4}\\) are yellow tangs. So the portion of all \ufb01sh in the aquarium yellow tangs are<br \/>\n\\(\\frac{2}{5}\\) X \\(\\frac{3}{4}\\),<br \/>\nStep I: We multiply the numerators as 2 X 3 = 6<br \/>\nStep II: We multiply the denominators as 5 X 4 = 20<br \/>\nStep III: We write the fraction in the simplest form as \\(\\frac{6}{20}\\),<br \/>\nwe can further simplify as both goes in 2, 2 X 3 = 6 and 2 X 10 = 20, (3,10),<span style=\"font-size: 16px;\">\\(\\frac{3}{10}\\).<br \/>\nSo \\(\\frac{2}{5}\\) X \\(\\frac{3}{4}\\) = \\(\\frac{3}{10}\\), therefore \\(\\frac{3}{10}\\) portion of all \ufb01sh in the aquarium are yellow tangs.<\/span><\/p>\n<p>Question 32.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nYou exercise for \\(\\frac{3}{4}\\) of an hour. You jump rope for \\(\\frac{1}{3}\\) of that time. What portion of the hour do you spend jumping rope?<br \/>\n\\(\\frac{1}{4}\\) of the hour I do spend jumping rope<\/p>\n<p>Explanation:<br \/>\nGiven I exercise for \\(\\frac{3}{4}\\) of an hour and I jump rope for \\(\\frac{1}{3}\\) of that time.<br \/>\nSo portion of the hour I do spend jumping rope is<br \/>\n\\(\\frac{3}{4}\\) X \\(\\frac{1}{3}\\),<br \/>\nStep I: We multiply the numerators as 3 X 1 = 3<br \/>\nStep II: We multiply the denominators as 4 X 3 = 12<br \/>\nStep III: We write the fraction in the simplest form as \\(\\frac{3}{12}\\),<br \/>\nwe can further simplify as both goes in 3, 3 X 1 = 3 and 3 X 4 = 12, (1,4),<br \/>\n<span style=\"font-size: 16px;\">\\(\\frac{1}{4}\\). So \\(\\frac{3}{4}\\) X \\(\\frac{1}{3}\\) = \\(\\frac{1}{4}\\), <\/span>Therefore \\(\\frac{1}{4}\\) of the hour I do spend jumping rope.<\/p>\n<p><strong>REASONING<\/strong><br \/>\n<strong>Without \ufb01nding the product, copy and complete the statement using &lt;, &gt;, or =. Explain your reasoning.<\/strong><\/p>\n<p>Question 33.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27095\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-57.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 57\" width=\"112\" height=\"49\" \/><br \/>\n&gt; as \\(\\frac{9}{10}\\) &lt; 1<\/p>\n<p>Explanation:<br \/>\nAs both sides we have \\(\\frac{4}{7}\\) both gets cancelled and we get 1 in left side<br \/>\nand \\(\\frac{9}{10}\\) in right side as we know 1 is greater than \\(\\frac{9}{10}\\)<br \/>\nso \\(\\frac{4}{7}\\) &gt; \\(\\frac{9}{10}\\) X \\(\\frac{4}{7}\\).<\/p>\n<p>Question 34.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27096\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-58.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 58\" width=\"112\" height=\"51\" \/><br \/>\n&gt; as \\(\\frac{22}{15}\\) &gt; 1<\/p>\n<p>Explanation:<br \/>\nAs both sides we have \\(\\frac{5}{8}\\) both gets cancelled and we get 1 in right side<br \/>\nand \\(\\frac{22}{15}\\) in left side as we know 1 is less than \\(\\frac{22}{15}\\)<br \/>\nas numerator is greater than denominator so \\(\\frac{5}{8}\\) X \\(\\frac{22}{15}\\) &gt;\u00a0 \\(\\frac{5}{8}\\).<\/p>\n<p>Question 35.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27097\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-59.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 59\" width=\"100\" height=\"57\" \/><br \/>\n= as \\(\\frac{7}{7}\\) = 1<br \/>\nExplanation:<br \/>\nAs both sides we have \\(\\frac{5}{6}\\) both gets cancelled and we get 1 in left side<br \/>\nand \\(\\frac{7}{7}\\) = 1 in right side as both are equal to 1, so \\(\\frac{5}{6}\\) = \\(\\frac{5}{6}\\) X \\(\\frac{7}{7}\\).<\/p>\n<p><strong>MULTIPLYING FRACTIONS AND MIXED NUMBERS<\/strong><br \/>\n<strong>Multiply. Write the answer in simplest form.<\/strong><\/p>\n<p>Question 36.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27098\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-60.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 60\" width=\"57\" height=\"47\" \/><br \/>\n<img decoding=\"async\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-60.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 60\" \/>= \\(\\frac{8}{9}\\)<br \/>\n1\\(\\frac{1}{3}\\) X \\(\\frac{2}{3}\\) = \\(\\frac{8}{9}\\)<\/p>\n<p>Explanation:<br \/>\nGiven 1 \\(\\frac{1}{3}\\) X \\(\\frac{2}{3}\\) so<br \/>\nfirst we write mixed number 1 \\(\\frac{1}{3}\\) as 1 X 3 + 1 by 3 = \\(\\frac{4}{3}\\) now we multiply \\(\\frac{4}{3}\\)\u00a0 X \u00a0\\(\\frac{2}{3}\\),<br \/>\nStep I: We multiply the numerators as 4 X 2 = 8<br \/>\nStep II: We multiply the denominators as 3 X 3 = 9<br \/>\nStep III: We write the fraction in the simplest form as \\(\\frac{8}{9}\\),<br \/>\nSo 1\\(\\frac{1}{3}\\) X \\(\\frac{2}{3}\\) = \\(\\frac{8}{9}\\).<\/p>\n<p>Question 37.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27099\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-61.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 61\" width=\"71\" height=\"50\" \/><br \/>\n<img decoding=\"async\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-61.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 61\" \/>= 2<br \/>\n6\\(\\frac{2}{3}\\) X \\(\\frac{3}{10}\\) = 2<\/p>\n<p>Explanation:<br \/>\nGiven 6\\(\\frac{2}{3}\\) X \\(\\frac{3}{10}\\) so<br \/>\nfirst we write mixed number 6\\(\\frac{2}{3}\\) as 6 X 3 + 2 by 3 = \\(\\frac{20}{3}\\) now we multiply \\(\\frac{20}{3}\\)\u00a0 X \u00a0\\(\\frac{3}{10}\\),<br \/>\nStep I: We multiply the numerators as 20 X 3 = 60<br \/>\nStep II: We multiply the denominators as 3 X 10 = 30<br \/>\nStep III: We write the fraction in the simplest form as \\(\\frac{60}{30}\\),<br \/>\nwe can further simplify as both goes in 30, 30 X 2 = 60 and 30 X 10 = 30, (2,1),<br \/>\nSo 6\\(\\frac{2}{3}\\) X \\(\\frac{3}{10}\\) = 2.<\/p>\n<p>Question 38.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27100\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-62.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 62\" width=\"65\" height=\"48\" \/><br \/>\n<img decoding=\"async\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-62.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 62\" \/>= 2<br \/>\n2\\(\\frac{1}{2}\\) X \\(\\frac{4}{5}\\) = 2<\/p>\n<p>Explanation:<br \/>\nGiven 2\\(\\frac{1}{2}\\) X \\(\\frac{4}{5}\\) so<br \/>\nfirst we write mixed number 6\\(\\frac{2}{3}\\) as 2 X 2 + 1 by 2 = \\(\\frac{5}{2}\\) now we multiply \\(\\frac{5}{2}\\)\u00a0 X \u00a0\\(\\frac{4}{5}\\),<br \/>\nStep I: We multiply the numerators as 5 X 4 = 20<br \/>\nStep II: We multiply the denominators as 2 X 5 = 10<br \/>\nStep III: We write the fraction in the simplest form as \\(\\frac{20}{10}\\),<br \/>\nwe can further simplify as both goes in 10, 10 X 2 = 20 and 10 X 1 = 10, (2,1),<br \/>\nSo 2\\(\\frac{1}{2}\\) X \\(\\frac{4}{5}\\) = 2.<\/p>\n<p>Question 39.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27101\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-63.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 63\" width=\"64\" height=\"49\" \/><br \/>\n<img decoding=\"async\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-63.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 63\" \/>= 2<\/p>\n<p>\\(\\frac{3}{5}\\) X 3\\(\\frac{1}{3}\\) = \\(\\frac{30}{15}\\) = 2.<\/p>\n<p>Explanation:<br \/>\nGiven \\(\\frac{3}{5}\\) X 3\\(\\frac{1}{3}\\) so<br \/>\nfirst we write mixed number 3\\(\\frac{1}{3}\\) as 3 X 3 + 1 by 3 = \\(\\frac{10}{3}\\) now we multiply \\(\\frac{3}{5}\\)\u00a0 X \u00a0\\(\\frac{10}{3}\\),<br \/>\nStep I: We multiply the numerators as 3 X 10 = 30<br \/>\nStep II: We multiply the denominators as 5 X 3 = 15<br \/>\nStep III: We write the fraction in the simplest form as \\(\\frac{30}{15}\\),<br \/>\nwe can further simplify as both goes in 15, 15 X 2 = 30 and 15 X 1 = 15, (2,1),<br \/>\nSo \\(\\frac{3}{5}\\) X 3\\(\\frac{1}{3}\\) = \\(\\frac{30}{15}\\) = 2.<\/p>\n<p>Question 40.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27102\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-64.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 64\" width=\"56\" height=\"48\" \/><br \/>\n<img decoding=\"async\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-64.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 64\" \/> = 5<\/p>\n<p>7\\(\\frac{1}{2}\\) X \\(\\frac{2}{3}\\) = \\(\\frac{30}{6}\\) = 5<\/p>\n<p>Explanation:<br \/>\nGiven 7\\(\\frac{1}{2}\\) X \\(\\frac{2}{3}\\) so<br \/>\nfirst we write mixed number 7\\(\\frac{1}{2}\\) as 7 X 2 + 1 by 2 = \\(\\frac{15}{2}\\) now we multiply \\(\\frac{15}{2}\\)\u00a0 X \u00a0\\(\\frac{2}{3}\\),<br \/>\nStep I: We multiply the numerators as 15 X 2 = 30<br \/>\nStep II: We multiply the denominators as 2 X 3 = 6<br \/>\nStep III: We write the fraction in the simplest form as \\(\\frac{30}{6}\\),<br \/>\nwe can further simplify as both goes in 6, 6 X 5 = 30 and 6 X 1 = 6, (5,1),<br \/>\nSo 7\\(\\frac{1}{2}\\) X \\(\\frac{2}{3}\\) = \\(\\frac{30}{6}\\) = 5.<\/p>\n<p>Question 41.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27103\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-65.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 65\" width=\"65\" height=\"45\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27103\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-65.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 65\" width=\"65\" height=\"45\" \/>= 2<\/p>\n<p>\\(\\frac{5}{9}\\) X 3\\(\\frac{3}{5}\\) = \\(\\frac{90}{45}\\) = 2.<\/p>\n<p>Explanation:<br \/>\nGiven \\(\\frac{5}{9}\\) X 3\\(\\frac{3}{5}\\) so<br \/>\nfirst we write mixed number 3\\(\\frac{3}{5}\\) as 3 X 5 + 3 by 5 = \\(\\frac{18}{5}\\) now we multiply \\(\\frac{5}{9}\\)\u00a0 X \u00a0\\(\\frac{18}{5}\\),<br \/>\nStep I: We multiply the numerators as 5 X 18 = 90<br \/>\nStep II: We multiply the denominators as 9 X 5 = 45<br \/>\nStep III: We write the fraction in the simplest form as \\(\\frac{90}{45}\\),<br \/>\nwe can further simplify as both goes in 45, 45 X 2 = 90 and 45 X 1 = 45, (2,1),<br \/>\nSo \\(\\frac{5}{9}\\) X 3\\(\\frac{3}{5}\\) = \\(\\frac{90}{45}\\) = 2.<\/p>\n<p>Question 42.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27104\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-66.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 66\" width=\"55\" height=\"48\" \/><br \/>\n<img decoding=\"async\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-66.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 66\" \/>= 1<\/p>\n<p>\\(\\frac{3}{4}\\) X 1\\(\\frac{1}{3}\\) = \\(\\frac{12}{12}\\) = 1<\/p>\n<p>Explanation:<br \/>\nGiven \\(\\frac{3}{4}\\) X 1\\(\\frac{1}{3}\\) so<br \/>\nfirst we write mixed number 1\\(\\frac{1}{3}\\) as 1 X 3 + 1 by 3 = \\(\\frac{4}{3}\\) now we multiply \\(\\frac{3}{4}\\)\u00a0 X \u00a0\\(\\frac{4}{3}\\),<br \/>\nStep I: We multiply the numerators as 3 X 4 = 12<br \/>\nStep II: We multiply the denominators as 4 X 3 = 12<br \/>\nStep III: We write the fraction in the simplest form as \\(\\frac{12}{12}\\),<br \/>\nwe can further simplify as both goes in 12, 12 X 1 = 12 and 12 X 1 = 12, (1,1),<br \/>\nSo \\(\\frac{3}{4}\\) X 1\\(\\frac{1}{3}\\) = \\(\\frac{12}{12}\\) = 1.<\/p>\n<p>Question 43.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27105\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-67.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 67\" width=\"64\" height=\"48\" \/><br \/>\n<img decoding=\"async\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-67.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 67\" \/>= \\(\\frac{3}{2}\\) = 1\\(\\frac{1}{2}\\)<\/p>\n<p>3\\(\\frac{3}{4}\\) X \\(\\frac{2}{5}\\) = \\(\\frac{3}{2}\\) = 1\\(\\frac{1}{2}\\)<\/p>\n<p>Explanation:<br \/>\nGiven 3\\(\\frac{3}{4}\\) X \\(\\frac{2}{5}\\) so<br \/>\nfirst we write mixed number 3\\(\\frac{3}{4}\\) as 3 X 4 + 3 by 4 = \\(\\frac{15}{4}\\) now we multiply \\(\\frac{15}{2}\\)\u00a0 X \u00a0\\(\\frac{2}{5}\\),<br \/>\nStep I: We multiply the numerators as 15 X 2 = 30<br \/>\nStep II: We multiply the denominators as 4 X 5 = 20<br \/>\nStep III: We write the fraction in the simplest form as \\(\\frac{30}{20}\\),<br \/>\nwe can further simplify as both goes in 10, 10 X 3 = 30 and 10 X 2 = 20, (3,2),<br \/>\nSo 3\\(\\frac{3}{4}\\) X \\(\\frac{2}{5}\\) = \\(\\frac{3}{2}\\).<br \/>\nAs numerator is greater than denominator we write in mixed fraction<br \/>\nalso as (1 X 2 + 1 by 2), 1 \\(\\frac{1}{2}\\).<\/p>\n<p>Question 44.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27106\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-68.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 68\" width=\"55\" height=\"49\" \/><br \/>\n<img decoding=\"async\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-68.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 68\" \/>= \\(\\frac{7}{2}\\) = 3\\(\\frac{1}{2}\\)<\/p>\n<p>4 \\(\\frac{3}{8}\\) X \\(\\frac{4}{5}\\) = \\(\\frac{7}{2}\\) = 3\\(\\frac{1}{2}\\)<\/p>\n<p>Explanation:<br \/>\nGiven 4\\(\\frac{3}{8}\\) X \\(\\frac{4}{5}\\) so<br \/>\nfirst we write mixed number 4\\(\\frac{3}{8}\\) as 8 X 4 + 3 by 8 = \\(\\frac{35}{8}\\) now we multiply \\(\\frac{35}{8}\\)\u00a0 X \u00a0\\(\\frac{4}{5}\\),<br \/>\nStep I: We multiply the numerators as 35 X 4 = 140<br \/>\nStep II: We multiply the denominators as 8 X 5 = 40<br \/>\nStep III: We write the fraction in the simplest form as \\(\\frac{140}{40}\\),<br \/>\nwe can further simplify as both goes in 20, 20 X 7 = 140 and 20 X 2 = 40, (7,2),<br \/>\nSo 4\\(\\frac{3}{8}\\) X \\(\\frac{4}{5}\\) = \\(\\frac{7}{2}\\).<br \/>\nAs numerator is greater than denominator we write in mixed fraction<br \/>\nalso as (3 X 2 + 1 by 2), 3\\(\\frac{1}{2}\\).<\/p>\n<p>Question 45.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27107\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-69.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 69\" width=\"66\" height=\"54\" \/><br \/>\n<img decoding=\"async\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-69.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 69\" \/>= \\(\\frac{17}{14}\\) = 1\\(\\frac{3}{14}\\)<\/p>\n<p>\\(\\frac{3}{7}\\) X 2\\(\\frac{5}{6}\\) = \\(\\frac{17}{14}\\) = 1\\(\\frac{3}{14}\\)<\/p>\n<p>Explanation:<br \/>\nGiven \\(\\frac{3}{7}\\) X 2\\(\\frac{5}{6}\\) so<br \/>\nfirst we write mixed number 2\\(\\frac{5}{6}\\) as 2 X 6 + 5 by 6 = \\(\\frac{17}{6}\\) now we multiply \\(\\frac{3}{7}\\)\u00a0 X \u00a0\\(\\frac{17}{6}\\),<br \/>\nStep I: We multiply the numerators as 17 X 3 = 51<br \/>\nStep II: We multiply the denominators as 7 X 6 = 42<br \/>\nStep III: We write the fraction in the simplest form as \\(\\frac{51}{42}\\),<br \/>\nwe can further simplify as both goes in 3, 3 X 17 = 51 and 3 X 14 = 12, (17,14),<br \/>\nSo \\(\\frac{3}{7}\\) X 2\\(\\frac{5}{6}\\) = \\(\\frac{17}{14}\\),<br \/>\nAs numerator is greater than denominator we write in mixed fraction<br \/>\nalso as (1 X 14 + 3 by 14), 1\\(\\frac{3}{14}\\).<\/p>\n<p>Question 46.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27108\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-70.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 70\" width=\"74\" height=\"53\" \/><br \/>\n<img decoding=\"async\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-70.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 70\" \/>= \\(\\frac{117}{5}\\) = 23\\(\\frac{2}{5}\\)<\/p>\n<p>1\\(\\frac{3}{10}\\) X 18 = \\(\\frac{117}{5}\\) = 23\\(\\frac{2}{5}\\)<\/p>\n<p>Explanation:<br \/>\nGiven 1\\(\\frac{3}{10}\\) X 18 so<br \/>\nfirst we write mixed number 1\\(\\frac{3}{10}\\) as 1 X 10\u00a0 + 3 by 10 = \\(\\frac{13}{10}\\) now we multiply \\(\\frac{13}{10}\\)\u00a0 X\u00a0 18,<br \/>\nStep I: We multiply the numerators as 13 X 18 = 234<br \/>\nStep II: Denominators will be same as 10<br \/>\nStep III: We write the fraction in the simplest form as \\(\\frac{234}{18}\\),<br \/>\nwe can further simplify as both goes in 2, 2 X 117 = 234 and 2 X 5 = 10, (117,5)<br \/>\nSo 1\\(\\frac{3}{10}\\) X 18 = \\(\\frac{117}{5}\\).<br \/>\nAs numerator is greater than denominator we write in mixed fraction<br \/>\nalso as (23 X 5 + 2 by 5), 23\\(\\frac{2}{5}\\).<\/p>\n<p>Question 47.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27109\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-71.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 71\" width=\"67\" height=\"44\" \/><br \/>\n<img decoding=\"async\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-71.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 71\" \/>=\u00a0\\(\\frac{110}{3}\\) = 36\\(\\frac{2}{3}\\)<\/p>\n<p>15 X 2\\(\\frac{4}{9}\\) = \\(\\frac{110}{3}\\) = 36\\(\\frac{2}{3}\\)<\/p>\n<p>Explanation:<br \/>\nGiven 15 X 2\\(\\frac{5}{6}\\) so first we write mixed number<br \/>\n2\\(\\frac{4}{9}\\) as 2 X 9 + 4 by 9 = \\(\\frac{22}{9}\\) now we multiply 15 X \u00a0\\(\\frac{22}{9}\\),<br \/>\nStep I: We multiply the numerators as 15 X 22 = 330<br \/>\nStep II: Denominator will be same as\u00a0 9<br \/>\nStep III: We write the fraction in the simplest form as \\(\\frac{330}{9}\\),<br \/>\nwe can further simplify as both goes in 3, 3 X 110 = 330 and 3 X 3 = 9, (110,3),<br \/>\nSo 15 X 2\\(\\frac{4}{9}\\) = \\(\\frac{110}{3}\\),<br \/>\nAs numerator is greater than denominator we write in mixed fraction<br \/>\nalso as (36 X 3 + 2 by 3), 36\\(\\frac{2}{3}\\).<\/p>\n<p>Question 48.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27110\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-72.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 72\" width=\"73\" height=\"50\" \/><br \/>\n<img decoding=\"async\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-72.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 72\" \/>= \\(\\frac{63}{8}\\) = 7\\(\\frac{7}{8}\\)<\/p>\n<p>Explanation:<br \/>\nGiven 1\\(\\frac{1}{6}\\) X 6\\(\\frac{3}{4}\\) so<br \/>\nfirst we write mixed numbers 1\\(\\frac{1}{6}\\) as 6 X 1 + 1 by 6 = \\(\\frac{7}{6}\\) and 6\\(\\frac{3}{4}\\) as 4 X 6 + 3 by 4 = \\(\\frac{27}{4}\\)<br \/>\nnow we multiply \\(\\frac{7}{6}\\)\u00a0 X \u00a0\\(\\frac{27}{4}\\),<br \/>\nStep I: We multiply the numerators as 7 X 27 = 189<br \/>\nStep II: We multiply the denominators as 6 X 4 = 24<br \/>\nStep III: We write the fraction in the simplest form as \\(\\frac{189}{24}\\),<br \/>\nwe can further simplify as both goes in 3, 3 X 63 = 189 and 3 X 8 = 24, (63,8),<br \/>\nSo 1\\(\\frac{1}{6}\\) X 6\\(\\frac{3}{4}\\) = \\(\\frac{63}{8}\\).<br \/>\nAs numerator is greater than denominator we write in mixed fraction<br \/>\nalso as (7 X 8 + 7 by 8 ), 7\\(\\frac{7}{8}\\).<\/p>\n<p>Question 49.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27111\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-73.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 73\" width=\"75\" height=\"42\" \/><br \/>\n<img decoding=\"async\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-73.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 73\" \/>= \\(\\frac{58}{9}\\) = 6\\(\\frac{4}{9}\\)<\/p>\n<p>Explanation:<br \/>\nGiven 2\\(\\frac{5}{12}\\) X 2\\(\\frac{2}{3}\\) so<br \/>\nfirst we write mixed numbers 2\\(\\frac{5}{12}\\) as 12 X 2 + 5 by 12 = \\(\\frac{29}{12}\\) and 2\\(\\frac{2}{3}\\) as 3 X 2 + 2 by 3 = \\(\\frac{8}{3}\\)<br \/>\nnow we multiply \\(\\frac{29}{12}\\)\u00a0 X \u00a0\\(\\frac{8}{3}\\),<br \/>\nStep I: We multiply the numerators as 29 X 8 = 232<br \/>\nStep II: We multiply the denominators as 12 X 3 = 36<br \/>\nStep III: We write the fraction in the simplest form as \\(\\frac{232}{36}\\),<br \/>\nwe can further simplify as both goes in 4, 4 X 58\u00a0 = 232 and 4 X 9 = 36, (58,9),<br \/>\nSo 2\\(\\frac{5}{12}\\) X 2\\(\\frac{2}{3}\\) = \\(\\frac{58}{9}\\).<br \/>\nAs numerator is greater than denominator we write in mixed fraction<br \/>\nalso as (6 X 9 + 4 by 9), 6\\(\\frac{4}{9}\\).<\/p>\n<p>Question 50.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27112\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-74.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 74\" width=\"69\" height=\"50\" \/><br \/>\n<img decoding=\"async\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-74.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 74\" \/> = \\(\\frac{125}{7}\\) = 17\\(\\frac{6}{7}\\)<\/p>\n<p>Explanation:<br \/>\nGiven 5\\(\\frac{5}{7}\\) X 3\\(\\frac{1}{8}\\) so<br \/>\nfirst we write mixed numbers 5\\(\\frac{5}{7}\\) as 7 X 5 + 5 by 7 = \\(\\frac{40}{7}\\) and 3\\(\\frac{1}{8}\\) as 8 X 3 + 1 by 8 = \\(\\frac{25}{8}\\)<br \/>\nnow we multiply \\(\\frac{40}{7}\\)\u00a0 X \u00a0\\(\\frac{25}{8}\\),<br \/>\nStep I: We multiply the numerators as 40 X 25 = 1000<br \/>\nStep II: We multiply the denominators as 7 X 8 = 56<br \/>\nStep III: We write the fraction in the simplest form as \\(\\frac{1000}{56}\\),<br \/>\nwe can further simplify as both goes in 8, 8 X 125 = 1000 and 8 X 7 = 56, (125,7),<br \/>\nSo 5\\(\\frac{5}{7}\\) X 3\\(\\frac{1}{8}\\) = \\(\\frac{125}{7}\\).<br \/>\nAs numerator is greater than denominator we write in mixed fraction<br \/>\nalso as (17 X 7 + 6 by 7), 17\\(\\frac{6}{7}\\).<\/p>\n<p>Question 51.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27113\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-75.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 75\" width=\"82\" height=\"51\" \/><br \/>\n<img decoding=\"async\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-75.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 75\" \/>= \\(\\frac{91}{8}\\) = 11\\(\\frac{3}{8}\\)<\/p>\n<p>Explanation:<br \/>\nGiven 2\\(\\frac{4}{5}\\) X 4\\(\\frac{1}{16}\\) so<br \/>\nfirst we write mixed numbers 2\\(\\frac{4}{5}\\) as 2 X 5 + 4 by 5 = \\(\\frac{14}{5}\\) and 4\\(\\frac{1}{16}\\) as 4 X 16 + 1 by 16 = \\(\\frac{65}{16}\\)<br \/>\nnow we multiply \\(\\frac{14}{5}\\)\u00a0 X \u00a0\\(\\frac{65}{16}\\),<br \/>\nStep I: We multiply the numerators as 14 X 65 = 910<br \/>\nStep II: We multiply the denominators as 5 X 16 = 80<br \/>\nStep III: We write the fraction in the simplest form as \\(\\frac{910}{80}\\),<br \/>\nwe can further simplify as both goes in 10, 10 X 91 = 910 and 10 X 8 = 80, (91,8),<br \/>\nSo 2\\(\\frac{4}{5}\\) X 4\\(\\frac{1}{16}\\) = \\(\\frac{91}{8}\\).<br \/>\nAs numerator is greater than denominator we write in mixed fraction<br \/>\nalso as (11 X 8 + 3 by 8 ), 11\\(\\frac{3}{8}\\).<\/p>\n<p><strong>YOU BE THE TEACHER<\/strong><br \/>\n<strong>Your friend \ufb01nds the product. Is your friend correct? Explain your reasoning.<\/strong><\/p>\n<p>Question 52.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27114\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-76.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 76\" width=\"198\" height=\"88\" \/><br \/>\nNo friend is incorrect.<br \/>\n4 X 3\\(\\frac{7}{10}\\) = 14\\(\\frac{8}{10}\\) \u2260 12\\(\\frac{7}{10}\\)<\/p>\n<p>Explanation:<br \/>\n4 X 3\\(\\frac{7}{10}\\) so first we write mixed numbers 3\\(\\frac{7}{10}\\)<br \/>\nas 3 X 10 + 7 by 10 = \\(\\frac{37}{10}\\)<br \/>\nnow we multiply 4 X \\(\\frac{37}{10}\\)<br \/>\nStep I: We multiply the numerators as 4 X 37 = 148<br \/>\nStep II: Denominator will be same as 10<br \/>\nStep III: We write the fraction in the simplest form as \\(\\frac{148}{10}\\),<br \/>\nSo 4 X 3\\(\\frac{7}{10}\\) = \\(\\frac{148}{10}\\),As numerator is greater than denominator we write in mixed fraction also as (14 X 10 + 8 by 10), 14\\(\\frac{8}{10}\\). As friend says 4 X 3\\(\\frac{7}{10}\\)\u00a0 =12\\(\\frac{7}{10}\\) which is incorrect<br \/>\nbecause 4 X 3\\(\\frac{7}{10}\\)\u00a0 = 14\\(\\frac{8}{10}\\). No friend is incorrect as<br \/>\n4 X 3\\(\\frac{7}{10}\\) = 14\\(\\frac{8}{10}\\) \u2260 12\\(\\frac{7}{10}\\)<\/p>\n<p>Question 53.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27115\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-77.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 77\" width=\"258\" height=\"158\" \/><\/p>\n<p>No friend is incorrect.<br \/>\n2\\(\\frac{1}{2}\\) X 7\\(\\frac{4}{5}\\) = 19\\(\\frac{1}{2}\\) \u2260 14\\(\\frac{2}{5}\\)<\/p>\n<p>Explanation:<br \/>\nGiven 2\\(\\frac{1}{2}\\) X 7\\(\\frac{4}{5}\\) so<br \/>\nfirst we write mixed numbers 2\\(\\frac{1}{2}\\) as 2 X 2 + 1 by 2 = \\(\\frac{5}{2}\\) and 7\\(\\frac{4}{5}\\) as 7 X 5 + 4 by 5 = \\(\\frac{39}{5}\\)<br \/>\nnow we multiply \\(\\frac{5}{2}\\)\u00a0 X \u00a0\\(\\frac{39}{5}\\),<br \/>\nStep I: We multiply the numerators as 5 X 39 = 195<br \/>\nStep II: We multiply the denominators as 2 X 5 = 10<br \/>\nStep III: We write the fraction in the simplest form as \\(\\frac{195}{10}\\),<br \/>\nwe can further simplify as both goes in 5, 5 X 39 = 195 and 5 X 2 = 10, (39,2),<br \/>\nSo 2\\(\\frac{1}{2}\\) X 7\\(\\frac{4}{5}\\) = \\(\\frac{39}{2}\\).<br \/>\nAs numerator is greater than denominator we write in mixed fraction<br \/>\nalso as (19 X 2 + 1 by 2), 19\\(\\frac{1}{2}\\).<br \/>\nAs friend says\u00a0 2\\(\\frac{1}{2}\\) X 7\\(\\frac{4}{5}\\) =14\\(\\frac{2}{5}\\) which is incorrect because 2\\(\\frac{1}{2}\\) X 7\\(\\frac{4}{5}\\) = 19\\(\\frac{1}{2}\\). No friend is incorrect as 2\\(\\frac{1}{2}\\) X 7\\(\\frac{4}{5}\\) = 19\\(\\frac{1}{2}\\) \u2260 14\\(\\frac{2}{5}\\).<\/p>\n<p>Question 54.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nA vitamin C tablet contains \\(\\frac{1}{4}\\) of a gram of vitamin C. You take 1\\(\\frac{1}{2}\\) tablets every day. How many grams of vitamin C do you take every day?<br \/>\n\\(\\frac{3}{8}\\) grams of vitamin C I do take every day.<\/p>\n<p>Explanation:<br \/>\nGiven a vitamin C tablet contains \\(\\frac{1}{4}\\) of a gram of vitamin C.<br \/>\nI take 1\\(\\frac{1}{2}\\) tablets every day. So number of grams of vitamin C<br \/>\nI do take every day is 1\\(\\frac{1}{2}\\) X \\(\\frac{1}{4}\\) so<br \/>\nfirst we write mixed number 1\\(\\frac{1}{2}\\) as 1 X 2\u00a0 + 1 by 2 =<br \/>\n\\(\\frac{3}{2}\\) now we multiply \\(\\frac{3}{2}\\)\u00a0 X\u00a0 \\(\\frac{1}{4}\\)<br \/>\nStep I: We multiply the numerators as 3 X 1 = 3<br \/>\nStep II: We multiply the denominators as 2 X 4 = 8<br \/>\nStep III: We write the fraction in the simplest form as \\(\\frac{3}{8}\\),<br \/>\nSo 1\\(\\frac{1}{2}\\) X \\(\\frac{1}{4}\\) = \\(\\frac{3}{8}\\).<br \/>\nTherefore \\(\\frac{3}{8}\\) grams of vitamin C I do take every day.<\/p>\n<p>Question 55.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nYou make a banner for a football rally.<br \/>\na. What is the area of the banner?<br \/>\nb. You add a \\(\\frac{1}{4}\\)-foot border on each side. What is the area of the new banner?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27116\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-78.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 78\" width=\"260\" height=\"110\" \/><\/p>\n<p>a. Area of the banner is 7 square feet<br \/>\nb. The area of new banner is 10\\(\\frac{15}{16}\\) square feet<\/p>\n<p>Explanation:<br \/>\na. Given width of banner as 4\\(\\frac{2}{3}\\) ft and height as 1\\(\\frac{1}{2}\\) feet,Therefore the area of banner is 4\\(\\frac{2}{3}\\) X 1\\(\\frac{1}{2}\\) so<br \/>\nfirst we write mixed numbers 4\\(\\frac{2}{3}\\) as 4 X 3 + 2 by 3 = \\(\\frac{14}{3}\\) and 1\\(\\frac{1}{2}\\) as 1 X 2 + 1 by 2 = \\(\\frac{3}{2}\\)<br \/>\nnow we multiply \\(\\frac{14}{3}\\)\u00a0 X \u00a0\\(\\frac{3}{2}\\),<br \/>\nStep I: We multiply the numerators as 14 X 3 = 42<br \/>\nStep II: We multiply the denominators as 3 X 2 = 6<br \/>\nStep III: We write the fraction in the simplest form as \\(\\frac{42}{6}\\),<br \/>\nwe can further simplify as both goes in 6, 6 X 7 = 42 and 6 X 1 = 6, (7,1),<br \/>\n4\\(\\frac{2}{3}\\) X 1\\(\\frac{1}{2}\\) = 7 square feet.<br \/>\nb. Now we add a \\(\\frac{1}{4}\\)-foot border on each side now the width changes to<br \/>\n\\(\\frac{14}{3}\\) X \\(\\frac{1}{4}\\) =\\(\\frac{14 x 1}{3 X 4}\\)= \\(\\frac{14}{12}\\) on simplification both goes in 2 we get \\(\\frac{7}{6}\\),<br \/>\nthe new width is \\(\\frac{14}{3}\\) + \\(\\frac{7}{6}\\) we get 14 x 2 + 7 by 6 = \\(\\frac{35}{6}\\) and new height changes to \\(\\frac{3}{2}\\) X \\(\\frac{1}{4}\\) = \\(\\frac{3}{8}\\) now the new height becomes \\(\\frac{3}{2}\\) + \\(\\frac{3}{8}\\) we get (3 X 4 + 3 by 8) = \\(\\frac{15}{8}\\), Now the area of the new banner is \\(\\frac{35}{6}\\) X \\(\\frac{15}{8}\\)<br \/>\nStep I: We multiply the numerators as 35 X 15 = 525<br \/>\nStep II: We multiply the denominators as 6 X 8 = 48<br \/>\nStep III: We write the fraction in the simplest form as \\(\\frac{525}{48}\\),<br \/>\nwe can further simplify as both goes in 3, 3 X 175 = 525 and 3 X 16 = 48, (175,16),<br \/>\n\\(\\frac{175}{16}\\), As numerator is greater than denominator we write in mixed fraction also as (10 X 16 + 15 by 16), 10\\(\\frac{15}{16}\\) square feet.<\/p>\n<p><strong>MULTIPLYING FRACTIONS AND MIXED NUMBERS<\/strong><br \/>\n<strong>Multiply. Write the answer in simplest form.<\/strong><\/p>\n<p>Question 56.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27117\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-79.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 79\" width=\"88\" height=\"43\" \/><br \/>\n<img decoding=\"async\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-79.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 79\" \/>= \\(\\frac{2}{15}\\)<\/p>\n<p>Explanation:<br \/>\nStep I: We multiply the numerators as 1 X 3 X 4 = 12<br \/>\nStep II: We multiply the denominators as 2 X 5 X 9 = 90<br \/>\nStep III: We write the fraction in the simplest form as \\(\\frac{12}{90}\\),<br \/>\nwe can further simplify as both goes in 6, 6 X 2 = 12 and 6 X 15 = 90, (2,15),<br \/>\nSo \\(\\frac{1}{2}\\) X \\(\\frac{3}{5}\\) X \\(\\frac{4}{9}\\) = \\(\\frac{2}{15}\\).<\/p>\n<p>Question 57.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27118\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-80.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 80\" width=\"86\" height=\"44\" \/><br \/>\n<img decoding=\"async\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-80.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 80\" \/>= \\(\\frac{25}{12}\\) = 2\\(\\frac{1}{12}\\)<br \/>\nExplanation:<br \/>\nGiven expression as \\(\\frac{4}{7}\\) X 4\\(\\frac{3}{8}\\) X \\(\\frac{5}{6}\\),<br \/>\nfirst we write mixed numbers 4\\(\\frac{3}{8}\\) as 4 X 8 + 3 by 8 = \\(\\frac{35}{8}\\) now we multiply \\(\\frac{4}{7}\\)\u00a0 X \u00a0\\(\\frac{35}{8}\\) X \\(\\frac{5}{6}\\)<br \/>\nStep I: We multiply the numerators as 4 X 35 X 5 = 700<br \/>\nStep II: We multiply the denominators as 7 X 8 X 6 = 336<br \/>\nStep III: We write the fraction in the simplest form as \\(\\frac{700}{336}\\),<br \/>\nwe can further simplify as both goes in 28, 28 X 25 = 700 and 28 X 12 = 336, (25,12),<br \/>\nSo \\(\\frac{4}{7}\\) X 4\\(\\frac{3}{8}\\) X \\(\\frac{5}{6}\\) = \\(\\frac{25}{12}\\), As numerator is greater than denominator we write in mixed fraction<br \/>\nalso as (2 X12 + 1 by 12), 2\\(\\frac{1}{12}\\).<\/p>\n<p>Question 58.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27119\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-81.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 81\" width=\"122\" height=\"46\" \/><br \/>\n<img decoding=\"async\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-81.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 81\" \/>= \\(\\frac{132}{5}\\) = 26\\(\\frac{2}{5}\\).<\/p>\n<p>Explanation:<br \/>\nGiven expression as 1\\(\\frac{1}{15}\\) X 5\\(\\frac{2}{5}\\) X 4\\(\\frac{7}{12}\\),first we write mixed numbers 1\\(\\frac{1}{15}\\) as 1 X 15 + 1 by 15 = \\(\\frac{16}{15}\\), 5\\(\\frac{2}{5}\\) as 5 X 5 + 2 by 5 = \\(\\frac{27}{5}\\),<br \/>\n4\\(\\frac{7}{12}\\) as 4 X 12 + 7 by 12 = 55 by 12 = \\(\\frac{55}{12}\\)<br \/>\nnow we multiply \\(\\frac{16}{15}\\) X \\(\\frac{27}{5}\\) X \\(\\frac{55}{12}\\)<br \/>\nStep I: We multiply the numerators as 16 X 27 X 55 = 23760<br \/>\nStep II: We multiply the denominators as 15 X 5 X 12 = 900<br \/>\nStep III: We write the fraction in the simplest form as \\(\\frac{23760}{900}\\),<br \/>\nwe can further simplify as both goes in 180, 180 X 132 = 23760 and 180 X 5 = 900, (132,5),<br \/>\nSo 1\\(\\frac{1}{15}\\) X 5\\(\\frac{2}{5}\\) X 4\\(\\frac{7}{12}\\) =<br \/>\n\\(\\frac{132}{5}\\). As numerator is greater than denominator we write in<br \/>\nmixed fraction also as (26 X 5 + 2 by 5), 26\\(\\frac{2}{5}\\).<\/p>\n<p>Question 59.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27120\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-82.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 82\" width=\"49\" height=\"48\" \/><br \/>\n<img decoding=\"async\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-82.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 82\" \/> = \\(\\frac{27}{125}\\)<br \/>\nExplanation:<br \/>\nGiven expression as (\\(\\frac{3}{5}\\))<sup>3 <\/sup>we write as\u00a0 \\(\\frac{3}{5}\\) X \\(\\frac{3}{5}\\) X \\(\\frac{3}{5}\\) now<br \/>\nStep I: We multiply the numerators as 3 X 3 X 3 = 27<br \/>\nStep II: We multiply the denominators as 5 X 5 X 5 = 125<br \/>\nStep III: We write the fraction in the simplest form as \\(\\frac{27}{125}\\).<br \/>\ntherefore (\\(\\frac{3}{5}\\))<sup>3 <\/sup>= (\\(\\frac{27}{125}\\)).<\/p>\n<p>Question 60.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27121\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-83.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 83\" width=\"96\" height=\"53\" \/><br \/>\n<img decoding=\"async\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-83.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 83\" \/>= \\(\\frac{9}{25}\\)<br \/>\nExplanation :<br \/>\nNow we write the expression as (\\(\\frac{4}{5}\\))<sup>2 <\/sup>X (\\(\\frac{3}{4}\\))<sup>2 <\/sup>=<br \/>\n\\(\\frac{4}{5}\\) X \\(\\frac{4}{5}\\) X \\(\\frac{3}{4}\\) X \\(\\frac{3}{4}\\) now Step I: We multiply the numerators as 4 X 4 X 3 X 3 = 144<br \/>\nStep II: We multiply the denominators as 5 X 5 X 4 X 4 = 400<br \/>\nStep III: We write the fraction in the simplest form as \\(\\frac{144}{400}\\)<br \/>\nwe can further simplify as both goes in 16, 16 X 9 = 144 and 16 X 25 = 400, (9,25),<br \/>\ntherefore (\\(\\frac{4}{5}\\))<sup>2 <\/sup>X (\\(\\frac{3}{4}\\))<sup>2 <\/sup>= \\(\\frac{9}{25}\\).<\/p>\n<p>Question 61.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27122\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-84.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 84\" width=\"104\" height=\"57\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27122\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-84.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 84\" width=\"104\" height=\"57\" \/>= \\(\\frac{121}{144}\\)<br \/>\nExplanation:<br \/>\nFirst we write mixed fraction into fraction as 1\\(\\frac{1}{10}\\) = 1 X 10 +1 by 10 =<br \/>\n\\(\\frac{11}{10}\\), Now we write (\\(\\frac{5}{6}\\))<sup>2 <\/sup>X (\\(\\frac{11}{10}\\))<sup>2 <\/sup>= \\(\\frac{5}{6}\\) X \\(\\frac{5}{6}\\) X \\(\\frac{11}{10}\\) X \\(\\frac{11}{10}\\) now Step I: We multiply the numerators as 5 X 5 X 11 X 11 = 3025<br \/>\nStep II: We multiply the denominators as 6 X 6 X 10 X 10 = 3600<br \/>\nStep III: We write the fraction in the simplest form as \\(\\frac{3025}{3600}\\),<br \/>\nwe can further simplify as both goes in 25, 25 X 121 = 3025 and 25 X 144 = 3600, (121,144),<br \/>\ntherefore (\\(\\frac{5}{6}\\))<sup>2 <\/sup>X (1\\(\\frac{1}{10}\\))<sup>2 <\/sup>= \\(\\frac{121}{144}\\).<\/p>\n<p>Question 62.<br \/>\n<strong>OPEN-ENDED<\/strong><br \/>\nFind a fraction that, when multiplied by \\(\\frac{1}{2}\\), is less than \\(\\frac{1}{4}\\).<br \/>\n\\(\\frac{1}{3}\\)<\/p>\n<p>Explanation:<br \/>\nLet us take on fraction as \\(\\frac{1}{3}\\) which when multiplied by \\(\\frac{1}{2}\\) we get numerator as 1 X 1 = 1 and denominator as 3 X 2 = 6 as \\(\\frac{1}{6}\\) &lt; \\(\\frac{1}{4}\\), So we take \\(\\frac{1}{3}\\) as<br \/>\n\\(\\frac{1}{3}\\) X \\(\\frac{1}{2}\\) &lt; \\(\\frac{1}{4}\\).<\/p>\n<p>Question 63.<br \/>\n<strong>LOGIC<\/strong><br \/>\nYou are in a bike race. When you get to the \ufb01rst checkpoint, you are \\(\\frac{2}{5}\\) of the distance to the second checkpoint. When you get to the second checkpoint, you are \\(\\frac{1}{4}\\) of the distance to the \ufb01nish. What is the distance from the start to the \ufb01rst checkpoint?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27123\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-85.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 85\" width=\"627\" height=\"119\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-85.png 627w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-85-300x57.png 300w\" sizes=\"(max-width: 627px) 100vw, 627px\" \/><br \/>\nThe distance from the start to the \ufb01rst checkpoint is 4 miles<\/p>\n<p>Explanation:<br \/>\nGiven total distance is 40 miles and first check point is \\(\\frac{2}{5}\\)<br \/>\nof the distance to the second checkpoint and second checkpoint is<br \/>\n\\(\\frac{1}{4}\\) of the distance to the \ufb01nish, So second checkpoint is \\(\\frac{1}{4}\\) X 40 as both goes in 4 we get 10 miles, At 10 miles we have second checkpoint,<br \/>\nnow\u00a0the distance from the start to the \ufb01rst checkpoint is \\(\\frac{2}{5}\\) X Second checkpoint \\(\\frac{2}{5}\\) X 10,<br \/>\nStep 1 : We multiply the numerators as 2 X 10<br \/>\nStep II: Denominator is 5,<br \/>\nStep III: We write the fraction in the simplest form as \\(\\frac{20}{5}\\)<br \/>\nwe can further simplify as both goes in 5, 5 X 4 = 20 and 5 X 1 = 5, (4,1) = 4 miles,<br \/>\ntherefore the distance from the start to the \ufb01rst checkpoint is 4 miles.<\/p>\n<p>Question 64.<br \/>\n<strong>NUMBER SENSE<\/strong><br \/>\nIs the product of two positive mixed numbers ever less than 1? Explain.<\/p>\n<p>No, the product of two positive mixed numbers never ever be less than 1,<\/p>\n<p>Explanation:<br \/>\nWe know a mixed must be greater than 1 and two numbers<br \/>\nthat are greater than one that are multiplied together end up<br \/>\nbeing greater that either number by itself. So the product of two<br \/>\npositive mixed numbers never ever be less than 1.<\/p>\n<p>Question 65.<br \/>\n<strong>REASONING<\/strong><br \/>\nYou plan to add a fountain to your garden.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27124\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-86.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 86\" width=\"327\" height=\"174\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-86.png 327w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-86-300x160.png 300w\" sizes=\"(max-width: 327px) 100vw, 327px\" \/><br \/>\na. Draw a diagram of the fountain in the garden. Label the dimensions.<br \/>\nb. Describe two methods for \ufb01nding the area of the garden that surrounds the fountain.<br \/>\nc. Find the area. Which method did you use, and why?<br \/>\na.<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-49604\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-20.bmp\" alt=\"\" width=\"341\" height=\"155\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-20.bmp 341w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-20-300x136.jpg 300w\" sizes=\"(max-width: 341px) 100vw, 341px\" \/><br \/>\nb. 1. Subtract area of the fountain from the total area of the garden or<br \/>\n2. We use rectangles to find the area of each piece of the garden and add these areas.<br \/>\nc. Area of the garden is 44\\(\\frac{3}{8}\\) square feet, Used<br \/>\nSubtract method because of fewer calculations.<\/p>\n<p>Explanation:<br \/>\na. We have taken measurements of fountain and drawn the fountain in the<br \/>\ngarden as shown with labels of width of fountain as 3\\(\\frac{1}{3}\\) and<br \/>\nheight of the fountain as 5\\(\\frac{1}{4}\\).<br \/>\nb. To find the area of the garden that surrounds the fountain first we<br \/>\nsubtract area of the fountain from the total area of the garden or<br \/>\nWe use rectangles to find the area of each piece of the garden and add these areas.<br \/>\nc. We use subtraction method first we calculate area of garden as<br \/>\n9\\(\\frac{1}{6}\\) X 6\\(\\frac{3}{4}\\)<br \/>\nFirst we write mixed fraction into fraction as 9\\(\\frac{1}{6}\\) = 9 X 6 + 1 by 6 =<br \/>\n\\(\\frac{55}{6}\\), 6\\(\\frac{3}{4}\\) = 6 X 4 + 3 by 4 = \\(\\frac{27}{4}\\) Now we multiply \\(\\frac{55}{6}\\) X \\(\\frac{27}{4}\\)<br \/>\nStep I: We multiply the numerators as 55 X 27 = 1485<br \/>\nStep II: We multiply the denominators as 6 X 4 = 24<br \/>\nStep III: We write the fraction in the simplest form as \\(\\frac{1485}{24}\\),<br \/>\nwe can further simplify as both goes in 3, 3 X 495 = 1485 and 3 X 8 = 24, (495,8),<br \/>\n9\\(\\frac{1}{6}\\) X 6\\(\\frac{3}{4}\\) = \\(\\frac{495}{8}\\).<\/p>\n<p>Now we calculate area of fountain as 5\\(\\frac{1}{4}\\) X 3 \\(\\frac{1}{3}\\),<br \/>\nFirst we write mixed fraction into fraction as 5\\(\\frac{1}{4}\\) = 5 X 4\u00a0 + 1 by 4 =<br \/>\n\\(\\frac{21}{4}\\) and 3 \\(\\frac{1}{3}\\) = 3 X 3 + 1 by 3 = \\(\\frac{10}{3}\\) ,Step I: We multiply the numerators as 21 X 10 = 210<br \/>\nStep II: We multiply the denominators as 4 X 3 = 12<br \/>\nStep III: We write the fraction in the simplest form as \\(\\frac{210}{12}\\),<br \/>\nwe can further simplify as both goes in 6, 6 X 35 = 210 and 6 X 2 = 12, (35,2),<br \/>\n5\\(\\frac{1}{4}\\) X 3\\(\\frac{1}{3}\\) = \\(\\frac{35}{2}\\).<br \/>\nTherefore area of garden is total area of garden &#8211; area of fountain so<br \/>\n\\(\\frac{495}{8}\\) &#8211; \\(\\frac{35}{2}\\) = (495 &#8211; 35 X 4) by 8 = \\(\\frac{355}{8}\\) ,As numerator is greater than denominator we write in<br \/>\nmixed fraction also as (44 X 8 + 3 by 8), 44\\(\\frac{3}{8}\\) square feet,<br \/>\nTherefore area of the garden is 44\\(\\frac{3}{8}\\) square feet,<br \/>\nHere we have used subtraction method because we can do fewer calculations.<\/p>\n<p>Question 66.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nThe cooking time for a ham is \\(\\frac{2}{5}\\) of an hour for each pound. What time should you start cooking a ham that weighs 12\\(\\frac{3}{4}\\) pounds so that it is done at 4:45 P.M.?<br \/>\nWe should start cooking at 11:39 am so that it is done at 4:45pm<\/p>\n<p>Explanation:<br \/>\nGiven the cooking time for a ham is \\(\\frac{2}{5}\\) of an hour for each pound,<br \/>\nThe minutes required is \\(\\frac{2}{5}\\)\u00a0 X 60 = 24 minutes,<br \/>\nso 24 minutes for each pound, Now we multiply minutes by pounds<br \/>\nFirst we write 12\\(\\frac{3}{4}\\) as 12 X 4 + 3 by 4 is \\(\\frac{51}{4}\\) X 24<br \/>\nStep I: We multiply the numerators as 51 X 24 =1224<br \/>\nStep II: Denominators is same 4<br \/>\nStep III: We write the fraction in the simplest form as \\(\\frac{1224}{4}\\), we get<br \/>\n306 as both goes in 4, Now we convert 306 minutes into hours as<br \/>\n\\(\\frac{306}{60}\\) = 5.1 and .1 in an hour is 6 minutes, Therefore<br \/>\nwe cook the ham for 5 hours and 6 minutes. As it is done at 4:45 pm means<br \/>\n16 hours,45 minutes &#8211; 5 hours 6 minutes = 11 : 39 am,<br \/>\nSo we should start cooking at 11:39 am.<\/p>\n<p>Question 67.<br \/>\n<strong>PRECISION<\/strong><br \/>\nComplete the Four Square for \\(\\frac{7}{8}\\) \u00d7 \\(\\frac{1}{3}\\).<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27125\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-87.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 87\" width=\"263\" height=\"177\" \/><br \/>\nAnswer is \\(\\frac{7}{24}\\)<br \/>\nMeaning is \\(\\frac{7}{8}\\) of \\(\\frac{1}{3}\\)<br \/>\nModel is<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-49660\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-21-1.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-21\" width=\"319\" height=\"235\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-21-1.bmp 319w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-21-1-300x221.jpg 300w\" sizes=\"(max-width: 319px) 100vw, 319px\" \/><br \/>\nApplication : The path around a park is \\(\\frac{1}{3}\\) mile long,<br \/>\nI walk \\(\\frac{7}{8}\\) of the path, How far did I walk?<\/p>\n<p>Explanation:<br \/>\nFirst we write answer as \\(\\frac{7}{8}\\) \u00d7 \\(\\frac{1}{3}\\) =<br \/>\nStep I: We multiply the numerators as 7 X 1 = 7<br \/>\nStep II: We multiply denominators as 8 X 3 = 24<br \/>\nStep III: We write the fraction in the simplest form as \\(\\frac{7}{24}\\),<br \/>\nSo \\(\\frac{7}{8}\\) \u00d7 \\(\\frac{1}{3}\\) = \\(\\frac{7}{24}\\)<br \/>\nThe meaning is \\(\\frac{7}{8}\\) of \\(\\frac{1}{3}\\) and Model is<br \/>\nas shown above the product is purple color overlapping 7 out of 24,<br \/>\nApplying the question as The path around a park is \\(\\frac{1}{3}\\) mile long,<br \/>\nI walk \\(\\frac{7}{8}\\) of the path, How far did I walk?<\/p>\n<p>Question 68.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nYou ask 150 people about their pets. The results show that \\(\\frac{9}{25}\\) of the people own a dog. Of the people who own a dog, \\(\\frac{1}{6}\\) of them also own a cat.<br \/>\na. What portion of the people own a dog and a cat?<br \/>\nb. How many people own a dog but not a cat? Explain.<\/p>\n<p>a. 54 people, 36% portion of the people own a dog and a cat.<br \/>\nb. 45 people own a dog but not a cat.<\/p>\n<p>Explanation:<br \/>\nGiven I ask 150 people about their pets, in that \\(\\frac{9}{25}\\) of the people own a dog means 150 X \\(\\frac{9}{25}\\) = \\(\\frac{1350}{25}\\) = 54 people own a dog. So portion of the people own a dog and cat in 150 are 54 X 100 by 150 = 36%.<br \/>\nNow Of the people who own a dog, \\(\\frac{1}{6}\\) of them also own a cat,<br \/>\nNumber of them also own a cat are 54 X \\(\\frac{1}{6}\\) = \\(\\frac{54}{6}\\)= 9<br \/>\nSo 9 people owns a cat. We have 54 people owns dog and cat ,<br \/>\nso only own a dog but not cat are 54 &#8211; 9 = 45 people own a dog but not a cat.<\/p>\n<p>Question 69.<br \/>\n<strong>NUMBER SENSE<\/strong><br \/>\nUse each of the numbers from 1 to 9 exactly once to create three mixed numbers with the greatest possible product. Then use each of the numbers exactly once to create three mixed numbers with the least possible product. Find each product. Explain your reasoning. The fraction portion of each mixed number should be proper.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27126\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-88.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 88\" width=\"220\" height=\"58\" \/><br \/>\nGreatest possible product is<br \/>\n9\\(\\frac{1}{2}\\) X 8\\(\\frac{3}{4}\\) X 7\\(\\frac{5}{6}\\) = 651\\(\\frac{7}{48}\\)<br \/>\nLeast possible product is<br \/>\n1\\(\\frac{4}{9}\\) X 2\\(\\frac{5}{8}\\) X 3\\(\\frac{6}{7}\\) = 14\\(\\frac{5}{8}\\)<\/p>\n<p>Explanation:<br \/>\nFirst we use the greatest digits for the whole numbers ,then we use<br \/>\nremaining digits to form the greatest(or least) fractional parts later<br \/>\nuse the least(or greatest) digits for the whole numbers ,<br \/>\nto calculate greatest possible product as<br \/>\n9\\(\\frac{1}{2}\\) X 8\\(\\frac{3}{4}\\) X 7\\(\\frac{5}{6}\\),<br \/>\nwe write mixed fraction as 9\\(\\frac{1}{2}\\) = 9 X 2 + 1 by 2 = \\(\\frac{19}{2}\\),<br \/>\n8\\(\\frac{3}{4}\\) = 8 X 4 + 3 by 4 = \\(\\frac{35}{4}\\), 7\\(\\frac{5}{6}\\) =<br \/>\n7 X 6 + 5 by 6 = \\(\\frac{47}{6}\\),Now we multiply \\(\\frac{19}{2}\\) X \\(\\frac{35}{4}\\) X \\(\\frac{47}{6}\\),<br \/>\nStep I: We multiply the numerators as 19 X 35 X 47 = 31255<br \/>\nStep II: We multiply denominators as 2 X 4 X 6 = 48<br \/>\nStep III: We write the fraction in the simplest form as \\(\\frac{31255}{48}\\),<br \/>\nAs numerator is greater than denominator we write in<br \/>\nmixed fraction also as (651 X 48 + 7 by 48), 651\\(\\frac{7}{48}\\),<\/p>\n<p>Now calculate least possible product as<br \/>\n1\\(\\frac{4}{9}\\) X 2\\(\\frac{5}{8}\\) X 3\\(\\frac{6}{7}\\),<br \/>\nwe write mixed fraction as 1\\(\\frac{4}{9}\\) = 1 X 9 + 4 by 9 = \\(\\frac{13}{9}\\),<br \/>\n2\\(\\frac{5}{8}\\) = 2 X 8 + 5 by 8 = \\(\\frac{21}{8}\\), 3\\(\\frac{6}{7}\\) =<br \/>\n3 X 7 + 6 by 7 = \\(\\frac{27}{7}\\),Now we multiply \\(\\frac{13}{9}\\) X \\(\\frac{21}{8}\\) X \\(\\frac{27}{7}\\)<br \/>\nStep I: We multiply the numerators as 13 X 21 X 27 = 7371<br \/>\nStep II: we multiply denominators as 9 X 8 X 7 = 504<br \/>\nStep III: We write the fraction in the simplest form as \\(\\frac{7371}{504}\\),<br \/>\nwe can further simplify as both goes in 63, 63 X 117 = 7371 and 63 X 8 = 504, (117,8) =<br \/>\n\\(\\frac{117}{8}\\),As numerator is greater than denominator we write in<br \/>\nmixed fraction also as (14 X 8 + 5 by 8), 14\\(\\frac{5}{8}\\).<\/p>\n<p>Therefore greatest possible product is 9\\(\\frac{1}{2}\\) X 8\\(\\frac{3}{4}\\) X 7\\(\\frac{5}{6}\\) = 651\\(\\frac{7}{48}\\),least possible product is 1\\(\\frac{4}{9}\\) X 2\\(\\frac{5}{8}\\) X 3\\(\\frac{6}{7}\\) = 14\\(\\frac{5}{8}\\).<\/p>\n<h3><a id=\"Lesson_2.2_Dividing_Fractions\"><\/a>Lesson 2.2 Dividing Fractions<\/h3>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p><strong>Dividing by Fractions<\/strong><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27127\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-89.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 89\" width=\"214\" height=\"231\" \/><br \/>\nWork with a partner. Answer each question using a model.<br \/>\na. How many two-thirds are in four?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27128\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-90.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 90\" width=\"445\" height=\"125\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-90.png 445w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-90-300x84.png 300w\" sizes=\"(max-width: 445px) 100vw, 445px\" \/><br \/>\nb. How many three-fourths are in three?<br \/>\nc. How many two-fifths are in four-fifths?<br \/>\nd. How many two-thirds are in three?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27129\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-91.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 91\" width=\"346\" height=\"124\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-91.png 346w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-91-300x108.png 300w\" sizes=\"(max-width: 346px) 100vw, 346px\" \/><br \/>\ne. How many one-thirds are in \ufb01ve-sixths?<br \/>\na.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-50043\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-22-4.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-22\" width=\"445\" height=\"228\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-22-4.bmp 445w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-22-4-300x154.jpg 300w\" sizes=\"(max-width: 445px) 100vw, 445px\" \/><br \/>\nSix, two-thirds are there in four,<br \/>\nb.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-50044\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-23-2.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-23\" width=\"343\" height=\"235\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-23-2.bmp 343w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-23-2-300x206.jpg 300w\" sizes=\"(max-width: 343px) 100vw, 343px\" \/><\/p>\n<p>Four, three-fourths are there in three,<br \/>\nc.<br \/>\n<a href=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-24-4.bmp\"><img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-50441\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-24-4.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-24\" width=\"628\" height=\"239\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-24-4.bmp 628w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-24-4-300x114.jpg 300w\" sizes=\"(max-width: 628px) 100vw, 628px\" \/><\/a><br \/>\nTwo, two-fifths are in four-fifths,<br \/>\nd.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-50438\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-25-1.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-25\" width=\"421\" height=\"197\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-25-1.bmp 421w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-25-1-300x140.jpg 300w\" sizes=\"(max-width: 421px) 100vw, 421px\" \/><br \/>\n4\\(\\frac{1}{2}\\), two-thirds are there in three,<br \/>\ne.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-50455\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-26-3.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-26\" width=\"722\" height=\"232\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-26-3.bmp 722w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-26-3-300x96.jpg 300w\" sizes=\"(max-width: 722px) 100vw, 722px\" \/><br \/>\n2\\(\\frac{1}{2}\\), one-thirds are in \ufb01ve-sixths<\/p>\n<p>Explanation:<br \/>\nThere are<br \/>\na. Given to find Two-Thirds are there in four is four divides \\(\\frac{2}{3}\\)<br \/>\nwe write reciprocal of the fraction \\(\\frac{2}{3}\\) as \\(\\frac{3}{2}\\)=<br \/>\n4\u00a0 X \\(\\frac{3}{2}\\) = \\(\\frac{12}{2}\\) =6,<br \/>\nSix, Two-Thirds are there in four as shown in the model above,<br \/>\nb. Given to find three-fourths are there in three is 3 divides\u00a0 \\(\\frac{3}{4}\\)<br \/>\nwe write reciprocal of the fraction \\(\\frac{3}{4}\\) as \\(\\frac{4}{3}\\)=<br \/>\n3 X \\(\\frac{4}{3}\\)= \\(\\frac{12}{3}\\) = 4<br \/>\nFour, three-fourths are there in three shown in the model above,<br \/>\nc. Given to find two-fifths are in four-fifths so four-fifths divides two -fifths,first we write<br \/>\n\\(\\frac{2}{5}\\) as reciprocal \\(\\frac{5}{2}\\) now multiply as<br \/>\n\\(\\frac{4}{5}\\) X \\(\\frac{5}{2}\\) = \\(\\frac{4 X 5}{5 X 2}\\) = 2<br \/>\nTwo, two-fifths are in four-fifths shown in the model above,<br \/>\nd. Given to find Two-Thirds are there in three is three divides \\(\\frac{2}{3}\\)<br \/>\nwe write reciprocal of the fraction \\(\\frac{2}{3}\\) as \\(\\frac{3}{2}\\)=<br \/>\n3\u00a0 X \\(\\frac{3}{2}\\) = \\(\\frac{9}{2}\\) as numerator is greater we write as<br \/>\n4 X 2 + 1 by 2 = 4\\(\\frac{1}{2}\\) \u00a04\\(\\frac{1}{2}\\), two-thirds are there in three shown in the model above,<br \/>\ne. Given to find one-thirds are in \ufb01ve-sixths first we write<br \/>\n\\(\\frac{1}{3}\\) as reciprocal \\(\\frac{3}{1}\\) now multiply as<br \/>\n\\(\\frac{5}{6}\\) X \\(\\frac{3}{1}\\) = \\(\\frac{5 X 3}{6 X 1}\\) = \\(\\frac{5}{2}\\)] as numerator is greater we write as<br \/>\n(2 X 2 + 1 by 2) = 2\\(\\frac{1}{2}\\),So 2\\(\\frac{1}{2}\\), one-thirds are in \ufb01ve-sixths as shown in the model above.<\/p>\n<p><strong>EXPLORATION 2<\/strong><\/p>\n<p><strong>Finding a Pattern<\/strong><br \/>\n<strong>Work with a partner. The table shows the division expressions from Exploration 1. Complete each multiplication expression so that it has the same value as the division expression above it. What can you conclude about dividing by fractions?<\/strong><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27130\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-92.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 92\" width=\"480\" height=\"116\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-92.png 480w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-92-300x73.png 300w\" sizes=\"(max-width: 480px) 100vw, 480px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27131\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-93.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 93\" width=\"155\" height=\"170\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-49692\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-27.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-27\" width=\"490\" height=\"126\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-27.bmp 490w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-27-300x77.jpg 300w\" sizes=\"(max-width: 490px) 100vw, 490px\" \/><br \/>\nExplanation:<br \/>\nDividing a fraction by another fraction is the same as multiplying the fraction<br \/>\nby the reciprocal (inverse) of the other. We get the reciprocal of a fraction<br \/>\nby interchanging its numerator and denominator.<br \/>\nYes the pattern found can be applied to division by a whole number as<br \/>\nStep 1: The whole number is converted into the fraction by<br \/>\napplying the denominator value as 1<br \/>\nStep 2: Take the reciprocal of the number<br \/>\nStep 3: Now, multiply the fractional value by a given fraction<br \/>\nStep 4: Simplify the given expression<\/p>\n<p><b>Example:<\/b> Divide \\(\\frac{6}{5}\\) by 10<br \/>\nStep 1: Convert 10 into a fraction: \\(\\frac{10}{1}\\)<br \/>\nStep 2: Take reciprocal: \\(\\frac{1}{10}\\)<br \/>\nStep 3: Multiply \\(\\frac{6}{5}\\) and \\(\\frac{1}{10}\\)<br \/>\nwe get \\(\\frac{6}{50}\\) on simplification as both goes in 2, 2 X 3 = 6 and 2 x 25 = 50,(3,25), So we get \\(\\frac{3}{25}\\).<\/p>\n<p><strong>2.2 Lesson<\/strong><\/p>\n<p>Two numbers whose product is 1 are reciprocals, or multiplicative inverses. To write the reciprocal of a number, \ufb01rst write the number as a fraction. Then invert the fraction. So, the reciprocal of a fraction \\(\\frac{a}{b}\\) is \\(\\frac{b}{a}\\), where a \u2260 0 and b \u2260 0.<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27132\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-94.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 94\" width=\"473\" height=\"280\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-94.png 473w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-94-300x178.png 300w\" sizes=\"(max-width: 473px) 100vw, 473px\" \/><\/p>\n<p><strong>Try It<\/strong><\/p>\n<p>Question 1.<br \/>\n\\(\\frac{3}{4}\\)<br \/>\n\\(\\frac{3}{4}\\) the reciprocals is\u00a0 \\(\\frac{4}{3}\\)<\/p>\n<p>Explanation:<br \/>\nWe write the reciprocals of \\(\\frac{3}{4}\\) as the number is already in fraction<br \/>\nwe write as \\(\\frac{4}{3}\\)<\/p>\n<p>Question 2.<br \/>\n5<br \/>\n5 the reciprocals is \\(\\frac{1}{5}\\)<br \/>\nExplanation:<br \/>\nWe write the reciprocals of 5 as the number is whole number we convert<br \/>\ninto the fraction by applying the denominator value as 1 and take<br \/>\nthe reciprocal of the number as \\(\\frac{1}{5}\\).<\/p>\n<p>Question 3.<br \/>\n\\(\\frac{7}{2}\\)<br \/>\n\\(\\frac{7}{2}\\) the reciprocals is\u00a0 \\(\\frac{2}{7}\\)<\/p>\n<p>Explanation:<br \/>\nWe write the reciprocals of \\(\\frac{7}{2}\\) as the number is already in fraction<br \/>\nwe write as \\(\\frac{2}{7}\\).<\/p>\n<p>Question 4.<br \/>\n\\(\\frac{4}{9}\\)<br \/>\n\\(\\frac{4}{9}\\) the reciprocals is\u00a0 \\(\\frac{9}{4}\\)<\/p>\n<p>Explanation:<br \/>\nWe write the reciprocals of \\(\\frac{4}{9}\\) as the number is already in fraction<br \/>\nwe write as \\(\\frac{9}{4}\\).<\/p>\n<p><strong>Key Idea<\/strong><br \/>\n<strong>Dividing Fractions<\/strong><br \/>\n<strong>Words<\/strong><br \/>\nTo divide a number by a fraction, multiply the number by the reciprocal of the fraction.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27133\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-95.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 95\" width=\"377\" height=\"96\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-95.png 377w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-95-300x76.png 300w\" sizes=\"(max-width: 377px) 100vw, 377px\" \/><\/p>\n<p>Divide. Write the answer in simplest form. Use a model to justify your answer.<\/p>\n<p>Question 5.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27134\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-96.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 96\" width=\"61\" height=\"44\" \/><br \/>\n<img decoding=\"async\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-96.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 96\" \/>= 4<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-49715\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-28-2.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-28\" width=\"427\" height=\"158\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-28-2.bmp 427w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-28-2-300x111.jpg 300w\" sizes=\"(max-width: 427px) 100vw, 427px\" \/><\/p>\n<p>Explanation:<br \/>\nGiven \\(\\frac{1}{2}\\) \u00f7 \\(\\frac{1}{8}\\) we write reciprocal of the fraction \\(\\frac{1}{8}\\) as \\(\\frac{8}{1}\\) and multiply as \\(\\frac{1}{2}\\) X 8 =\\(\\frac{8}{2}\\) = 4. As shown in the model we take half of 8 we get 4.<\/p>\n<p>Question 6.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27135\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-97.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 97\" width=\"63\" height=\"49\" \/><br \/>\n<img decoding=\"async\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-97.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 97\" \/>= 1\\(\\frac{1}{3}\\)<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-49699\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-29.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-29\" width=\"465\" height=\"158\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-29.bmp 465w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-29-300x102.jpg 300w\" sizes=\"(max-width: 465px) 100vw, 465px\" \/><\/p>\n<p>Explanation:<br \/>\nGiven \\(\\frac{2}{5}\\) \u00f7 \\(\\frac{3}{10}\\) we write reciprocal of the fraction \\(\\frac{3}{10}\\) as \\(\\frac{10}{3}\\) and multiply as \\(\\frac{2}{5}\\) X<br \/>\n\\(\\frac{10}{3}\\)=\\(\\frac{2 X 10 }{5 X 3}\\) = \\(\\frac{4}{3}\\) = 1\\(\\frac{1}{3}\\) and we have shown in the area model above.<\/p>\n<p>Question 7.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27136\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-98.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 98\" width=\"80\" height=\"50\" \/><br \/>\n<img decoding=\"async\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-98.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 98\" \/>=\u00a0 \\(\\frac{1}{2}\\)<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-49712\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-30.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-30\" width=\"506\" height=\"211\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-30.bmp 506w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-30-300x125.jpg 300w\" sizes=\"(max-width: 506px) 100vw, 506px\" \/><br \/>\nExplanation:<br \/>\nGiven \\(\\frac{3}{8}\\) \u00f7 \\(\\frac{3}{4}\\) we write reciprocal of the fraction \\(\\frac{3}{4}\\) as \\(\\frac{4}{3}\\) and multiply as \\(\\frac{3}{8}\\) X<br \/>\n\\(\\frac{4}{3}\\) = \\(\\frac{3 X 4 }{8 X 3}\\) = \\(\\frac{1}{2}\\)<br \/>\nand we have shown in the area model as above.<br \/>\nQuestion 8.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27137\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-99.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 99\" width=\"63\" height=\"51\" \/><br \/>\n<img decoding=\"async\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-99.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 99\" \/>= \\(\\frac{4}{9}\\)<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-49722\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-31-1.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-31\" width=\"759\" height=\"226\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-31-1.bmp 759w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-31-1-300x89.jpg 300w\" sizes=\"(max-width: 759px) 100vw, 759px\" \/><br \/>\nExplanation:<br \/>\nGiven \\(\\frac{2}{7}\\) \u00f7 \\(\\frac{9}{14}\\) we write reciprocal of the fraction \\(\\frac{9}{14}\\) as \\(\\frac{14}{9}\\) and multiply as \\(\\frac{2}{7}\\) X<br \/>\n\\(\\frac{14}{9}\\) = \\(\\frac{2 X 14 }{7 X 9}\\) = \\(\\frac{4}{9}\\)<br \/>\nand we have shown in the area model above.<\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Divide. Write the answer in simplest form.<\/strong><\/p>\n<p>Question 9.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27138\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-100.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 100\" width=\"58\" height=\"45\" \/><br \/>\n<img decoding=\"async\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-100.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 100\" \/>= \\(\\frac{1}{9}\\)<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{1}{3}\\)\u00f7 3 as the number 3 is whole number we convert<br \/>\ninto the fraction by applying the denominator value as 1 and take<br \/>\nthe reciprocal of the number as \\(\\frac{1}{3}\\) and multiply as \\(\\frac{1}{3}\\) X \\(\\frac{1}{3}\\) Step I: We multiply the numerators as 1 X 1 = 1<br \/>\nStep II: We multiply denominators as 3 X 3 = 9<br \/>\nStep III: We write the fraction in the simplest form as \\(\\frac{1}{9}\\),<br \/>\nSo \\(\\frac{1}{3}\\)\u00f7 3 = \\(\\frac{1}{9}\\).<\/p>\n<p>Question 10.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27139\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-101.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 101\" width=\"56\" height=\"45\" \/><br \/>\n<img decoding=\"async\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-101.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 101\" \/>= \\(\\frac{1}{15}\\)<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{2}{3}\\)\u00f7 10 as the number 10 is whole number we convert<br \/>\ninto the fraction by applying the denominator value as 1 and take<br \/>\nthe reciprocal of the number as \\(\\frac{1}{10}\\) and multiply as \\(\\frac{2}{3}\\) X \\(\\frac{1}{10}\\) Step I: We multiply the numerators as 2 X 1 = 2<br \/>\nStep II: We multiply denominators as 3 X 10 = 30<br \/>\nStep III: We write the fraction in the simplest form as \\(\\frac{2}{30}\\),<br \/>\nwe can further simplify as both goes in 2, 2 X 1 = 2 and 2 X 15 = 30, (1,15) =<br \/>\nSo \\(\\frac{2}{3}\\)\u00f7 10 = \\(\\frac{1}{15}\\).<\/p>\n<p>Question 11.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27140\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-102.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 102\" width=\"55\" height=\"44\" \/><br \/>\n<img decoding=\"async\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-102.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 102\" \/>= \\(\\frac{5}{32}\\)<\/p>\n<p>Explanation:<br \/>\n\\(\\frac{5}{8}\\)\u00f7 4 as the number 4 is whole number we convert<br \/>\ninto the fraction by applying the denominator value as 1 and take<br \/>\nthe reciprocal of the number as \\(\\frac{1}{4}\\) and multiply as \\(\\frac{5}{8}\\) X \\(\\frac{1}{4}\\) Step I: We multiply the numerators as 5 X 1 = 5<br \/>\nStep II: We multiply denominators as 8 X 4 = 32<br \/>\nStep III: We write the fraction in the simplest form as \\(\\frac{5}{32}\\),<br \/>\nSo \\(\\frac{5}{8}\\)\u00f7 4 = \\(\\frac{5}{32}\\).<\/p>\n<p>Question 12.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27141\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-103.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 103\" width=\"59\" height=\"51\" \/><br \/>\n<img decoding=\"async\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-103.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 103\" \/>= \\(\\frac{3}{14}\\)<br \/>\nExplanation:<br \/>\n\\(\\frac{6}{7}\\)\u00f7 4 as the number 4 is whole number we convert<br \/>\ninto the fraction by applying the denominator value as 1 and take<br \/>\nthe reciprocal of the number as \\(\\frac{1}{4}\\) and multiply as \\(\\frac{6}{7}\\) X \\(\\frac{1}{4}\\) Step I: We multiply the numerators as 6 X 1 = 6<br \/>\nStep II: We multiply denominators as 7 X 4 = 28<br \/>\nStep III: We write the fraction in the simplest form as \\(\\frac{6}{28}\\),<br \/>\nwe can further simplify as both goes in 2, 2 X 3 = 6 and 2 X 14 = 28, (3,14) =<br \/>\nSo \\(\\frac{6}{7}\\)\u00f7 4 = \\(\\frac{3}{14}\\).<\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><\/p>\n<p>Solve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p><strong>DIVIDING FRACTIONS<\/strong><br \/>\n<strong>Divide. Write the answer in simplest form. Draw a model to justify your answer.<\/strong><\/p>\n<p>Question 13.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27142\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-104.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 104\" width=\"55\" height=\"46\" \/><br \/>\n<img decoding=\"async\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-104.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 104\" \/>=\\(\\frac{12}{15}\\)= \\(\\frac{4}{5}\\)<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-49872\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-32.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-32\" width=\"796\" height=\"325\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-32.bmp 796w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-32-300x122.jpg 300w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-32-768x314.jpg 768w\" sizes=\"(max-width: 796px) 100vw, 796px\" \/><\/p>\n<p>Explanation:<br \/>\nGiven \\(\\frac{2}{3}\\) \u00f7 \\(\\frac{5}{6}\\) we write reciprocal of the fraction \\(\\frac{5}{6}\\) as \\(\\frac{6}{5}\\) and multiply as \\(\\frac{2}{3}\\) X<br \/>\n\\(\\frac{6}{5}\\) = \\(\\frac{2 X 6}{3 X 5}\\) = \\(\\frac{12}{15}\\)<br \/>\nwe can further simplify as both goes in 3, 3 X 4 = 12 and 3 X 5 = 15, (4,5) = \\(\\frac{4}{5}\\).<\/p>\n<p>Question 14.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27143\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-105.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 105\" width=\"55\" height=\"46\" \/><br \/>\n<img decoding=\"async\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-105.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 105\" \/>= \\(\\frac{2}{7}\\)<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-49879\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-34.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-34\" width=\"706\" height=\"272\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-34.bmp 706w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-34-300x116.jpg 300w\" sizes=\"(max-width: 706px) 100vw, 706px\" \/><\/p>\n<p>Explanation:<br \/>\n\\(\\frac{6}{7}\\)\u00f7 3 as the number 3 is whole number we convert<br \/>\ninto the fraction by applying the denominator value as 1 and take<br \/>\nthe reciprocal of the number as \\(\\frac{1}{3}\\) and multiply as \\(\\frac{6}{7}\\) X \\(\\frac{1}{3}\\) Step I: We multiply the numerators as 6 X 1 = 6<br \/>\nStep II: We multiply denominators as 7 X 3 = 21<br \/>\nStep III: We write the fraction in the simplest form as \\(\\frac{6}{21}\\),<br \/>\nwe can further simplify as both goes in 3, 3 X 2 = 6 and 3 X 7 = 21, (2,7),<br \/>\nSo \\(\\frac{6}{7}\\)\u00f7 3 = \\(\\frac{2}{7}\\).<\/p>\n<p>Question 15.<br \/>\n<strong>WHICH ONE DOESN\u2019T BELONG?<\/strong><br \/>\nWhich of the following does not belong with the other three? Explain your reasoning.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27144\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-106.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 106\" width=\"365\" height=\"73\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-106.png 365w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-106-300x60.png 300w\" sizes=\"(max-width: 365px) 100vw, 365px\" \/><br \/>\n\\(\\frac{3}{2}\\) X \\(\\frac{4}{5}\\) does not belong with the other three<\/p>\n<p>Explanation:<br \/>\na. \\(\\frac{2}{3}\\) \u00f7 \\(\\frac{4}{5}\\) we write reciprocal of the fraction \\(\\frac{4}{5}\\) as \\(\\frac{5}{4}\\) and multiply as \\(\\frac{2}{3}\\) X<br \/>\n\\(\\frac{5}{4}\\) = \\(\\frac{2 X 5}{3 X 4}\\)\u00a0 = \\(\\frac{10}{12}\\)<br \/>\nwe can further simplify as both goes in 2, 2 X 5 = 10 and 2 X 6 = 12, (5,6),<br \/>\n\\(\\frac{2}{3}\\) \u00f7 \\(\\frac{4}{5}\\) = \\(\\frac{5}{6}\\).<br \/>\nb. \\(\\frac{3}{2}\\) X \\(\\frac{4}{5}\\) = \\(\\frac{3 X 4}{2 X 5}\\)\u00a0 =\\(\\frac{12}{10}\\) we can further simplify as both goes in 2, 2 X 6 = 12 and 2 X 5 = 10, (6,5), \\(\\frac{6}{5}\\).<br \/>\nc. \\(\\frac{5}{4}\\) X \\(\\frac{2}{3}\\) = \\(\\frac{5 X 2}{4 X 3}\\) =<br \/>\n\\(\\frac{10}{12}\\) we can further simplify as both goes in 2, 2 X 5 = 10 and 2 X 6 = 12, (5,6),\\(\\frac{5}{4}\\) X \\(\\frac{2}{3}\\) = \\(\\frac{5}{6}\\).<br \/>\nd. \\(\\frac{5}{4}\\) \u00f7 \\(\\frac{3}{2}\\) we write reciprocal of the fraction \\(\\frac{3}{2}\\) as \\(\\frac{2}{3}\\) and multiply as \\(\\frac{5}{4}\\) X<br \/>\n\\(\\frac{2}{3}\\) = \\(\\frac{5 X 2}{4 X 3}\\)\u00a0 = \\(\\frac{10}{12}\\)<br \/>\nwe can further simplify as both goes in 2, 2 X 5 = 10 and 2 X 6 = 12, (5,6),<br \/>\n\\(\\frac{5}{4}\\) \u00f7 \\(\\frac{3}{2}\\) = \\(\\frac{5}{6}\\).<br \/>\nAs \\(\\frac{2}{3}\\) \u00f7 \\(\\frac{4}{5}\\), \\(\\frac{5}{4}\\) X \\(\\frac{2}{3}\\), \\(\\frac{5}{4}\\) \u00f7 \\(\\frac{3}{2}\\) = \\(\\frac{5}{6}\\) only<br \/>\n\\(\\frac{3}{2}\\) X \\(\\frac{4}{5}\\) = \\(\\frac{6}{5}\\),<br \/>\nso \\(\\frac{3}{2}\\) X \\(\\frac{4}{5}\\) does not belong with the other three.<\/p>\n<p><strong>MATCHING<\/strong><br \/>\n<strong>Match the expression with its value.<\/strong><\/p>\n<p>Question 16.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27145\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-107.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 107\" width=\"64\" height=\"96\" \/><br \/>\n\\(\\frac{2}{5}\\) \u00f7 \\(\\frac{8}{15}\\) =\\(\\frac{3}{4}\\) matches with B<\/p>\n<p>Explanation:<br \/>\nGiven expressions as \\(\\frac{2}{5}\\) \u00f7 \\(\\frac{8}{15}\\) we write reciprocal of the fraction \\(\\frac{8}{15}\\) as \\(\\frac{15}{8}\\) and multiply as \\(\\frac{2}{5}\\) X \\(\\frac{15}{8}\\) = \\(\\frac{2 X 15}{5 X 8}\\) = \\(\\frac{30}{40}\\),we can further simplify as both goes in 10, 10 X 3 = 30 and 10 X 4 = 40, (3,4),<br \/>\n\\(\\frac{3}{4}\\) therefore \\(\\frac{2}{5}\\) \u00f7 \\(\\frac{8}{15}\\) =\\(\\frac{3}{4}\\) matches with B.<\/p>\n<p>Question 17.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27146\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-108.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 108\" width=\"69\" height=\"97\" \/><br \/>\n\\(\\frac{8}{15}\\) \u00f7 \\(\\frac{2}{5}\\) = 1\\(\\frac{1}{3}\\) matches with D<\/p>\n<p>Explanation:<br \/>\nGiven expressions as \\(\\frac{8}{15}\\) \u00f7 \\(\\frac{2}{5}\\) we write reciprocal of the fraction \\(\\frac{2}{5}\\) as \\(\\frac{5}{2}\\) and multiply as \\(\\frac{8}{15}\\) X \\(\\frac{5}{2}\\) = \\(\\frac{8 X 5}{15 X 2}\\) = \\(\\frac{40}{30}\\),we can further simplify as both goes in 10, 10 X 4 = 40 and 10 X 3 = 30, (4,3),<br \/>\n\\(\\frac{4}{3}\\) As numerator is greater than denominator we write in<br \/>\nmixed fraction also as (1 X 3 + 1 by 3), 1\\(\\frac{1}{3}\\), therefore \\(\\frac{8}{15}\\) \u00f7 \\(\\frac{2}{5}\\) = 1\\(\\frac{1}{3}\\) matches with D.<\/p>\n<p>Question 18.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27147\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-109.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 109\" width=\"77\" height=\"92\" \/><br \/>\n\\(\\frac{2}{15}\\) \u00f7 \\(\\frac{8}{5}\\) =\\(\\frac{1}{12}\\) matches with A<\/p>\n<p>Explanation:<br \/>\nGiven expressions as \\(\\frac{2}{15}\\) \u00f7 \\(\\frac{8}{5}\\) we write reciprocal of the fraction \\(\\frac{8}{5}\\) as \\(\\frac{5}{8}\\) and multiply as \\(\\frac{2}{15}\\) X \\(\\frac{5}{8}\\) = \\(\\frac{2 X 5}{15 X 8}\\) = \\(\\frac{10}{120}\\),we can further simplify as both goes in 10, 10 X 1 = 10 and 10 X 12= 120, (1,12),<br \/>\n\\(\\frac{1}{12}\\) ,therefore \\(\\frac{2}{15}\\) \u00f7 \\(\\frac{8}{5}\\) =\\(\\frac{1}{12}\\) matches with A.<\/p>\n<p>Question 19.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27148\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-110.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 110\" width=\"74\" height=\"99\" \/><br \/>\n\\(\\frac{8}{5}\\) \u00f7 \\(\\frac{2}{15}\\) = 12 matches with C<\/p>\n<p>Explanation:<br \/>\nGiven expressions as \\(\\frac{8}{5}\\) \u00f7 \\(\\frac{2}{15}\\) we write reciprocal of the fraction \\(\\frac{2}{15}\\) as \\(\\frac{15}{2}\\) and multiply as \\(\\frac{8}{5}\\) X \\(\\frac{15}{2}\\) = \\(\\frac{8 X 15}{5 X 2}\\) = \\(\\frac{120}{10}\\),we can further simplify as both goes in 10, 10 X 12 = 120 and 10 X 1 = 10, (12,1),= 12,<br \/>\nSo \\(\\frac{8}{5}\\) \u00f7 \\(\\frac{2}{15}\\) = 12 matches with C.<\/p>\n<p><strong>Self-Assessment for Problem Solving<\/strong><\/p>\n<p>Solve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 20.<br \/>\nYou have 5 cups of rice to make bibimbap, a popular Korean meal. The recipe calls for \\(\\frac{4}{5}\\) cup of rice per serving. How many full servings of bibimbap can you make? How much rice is left over?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27186\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-111.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 111\" width=\"224\" height=\"178\" \/><\/p>\n<p>6 full servings of bibimbap I can make, \\(\\frac{1}{4}\\) cup of rice is left over<\/p>\n<p>Explanation:<br \/>\nGiven I have 5 cups of rice to make bibimbap, a popular Korean meal and<br \/>\nthe recipe calls for \\(\\frac{4}{5}\\) cup of rice per serving so we divide 5 cups with<br \/>\n\\(\\frac{4}{5}\\) cup of rice per serving as 5 \u00f7 \\(\\frac{4}{5}\\) we write reciprocal of the fraction \\(\\frac{4}{5}\\) as \\(\\frac{5}{4}\\) and multiply as<br \/>\n5 X \\(\\frac{5}{4}\\), Step I: We multiply the numerators as 5 X 5 = 25<br \/>\nStep II: Denominator is same 4<br \/>\nStep III: We write the fraction in the simplest form as \\(\\frac{25}{4}\\),<br \/>\nAs numerator is greater than denominator we write in<br \/>\nmixed fraction also as ( 6 X 4 + 1 by 4), 6\\(\\frac{1}{4}\\) we got whole as 6, therefore<br \/>\n6 full servings of bibimbap I can make and \\(\\frac{1}{4}\\) cup of rice is left over.<\/p>\n<p>Question 21.<br \/>\nA band earns \\(\\frac{2}{3}\\) of their pro\ufb01t from selling concert tickets and \\(\\frac{1}{5}\\) of their pro\ufb01t from selling merchandise. The band earns a pro\ufb01t of $1500 from selling concert tickets. How much pro\ufb01t does the band earn from selling merchandise?<\/p>\n<p>$450 profit does the band earn from selling merchandise<\/p>\n<p>Explanation :<br \/>\nLet us take the amount be x and a band earns \\(\\frac{2}{3}\\) of their pro\ufb01t from selling concert tickets and makes a pro\ufb01t of $1500 from selling concert tickets,<br \/>\nSo x X \\(\\frac{2}{3}\\) = $1500, on simplification 2x = 1500 X 3 = 4500,<br \/>\ntherefore x = \\(\\frac{4500}{2}\\) = $2250 and \\(\\frac{1}{5}\\) of their pro\ufb01t from selling merchandise means $2250 X \\(\\frac{1}{5}\\) = \\(\\frac{2250}{5}\\)=<br \/>\n$450.<\/p>\n<h3><a id=\"Dividing_Fractions_Homework_&amp;_Practice_2.2\"><\/a>Dividing Fractions Homework &amp; Practice 2.2<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Multiply. Write the answer in simplest form.<\/strong><\/p>\n<p>Question 1.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27187\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-112.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 112\" width=\"51\" height=\"47\" \/><br \/>\n<img decoding=\"async\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-112.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 112\" \/>= \\(\\frac{21}{40}\\)<br \/>\nExplanation:<br \/>\nGiven expression as \\(\\frac{7}{10}\\) X \\(\\frac{3}{4}\\),<br \/>\nStep I: We multiply the numerators as 7 X 3 = 21<br \/>\nStep II: We multiply denominators as 10 X 4 = 40<br \/>\nStep III: We write the fraction in the simplest form as \\(\\frac{21}{40}\\),<br \/>\nSo \\(\\frac{7}{10}\\) X \\(\\frac{3}{4}\\) = \\(\\frac{21}{40}\\).<\/p>\n<p>Question 2.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27188\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-113.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 113\" width=\"61\" height=\"42\" \/><br \/>\n<img decoding=\"async\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-113.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 113\" \/>= 1\\(\\frac{17}{18}\\)<br \/>\nExplanation:<br \/>\nGiven \\(\\frac{5}{6}\\) X 2\\(\\frac{1}{3}\\) so<br \/>\nfirst we write mixed number 2\\(\\frac{1}{3}\\)\u00a0 as 2 X 3 + 1 by 3 =<br \/>\n\\(\\frac{7}{3}\\) now<br \/>\nwe multiply \\(\\frac{5}{6}\\)\u00a0 X \u00a0\\(\\frac{7}{3}\\),<br \/>\nStep I: We multiply the numerators as 5 X 7 = 35<br \/>\nStep II: We multiply the denominators as 6 X 3 =18<br \/>\nStep III: We write the fraction in the simplest form as \\(\\frac{35}{18}\\),<br \/>\nAs numerator is greater than denominator we write in<br \/>\nmixed fraction also as ( 1 X 18 + 17 by 18 ), 1\\(\\frac{17}{18}\\)<br \/>\nSo \\(\\frac{5}{6}\\) X 2\\(\\frac{1}{3}\\) = 1\\(\\frac{17}{18}\\).<\/p>\n<p>Question 3.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27189\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-114.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 114\" width=\"53\" height=\"48\" \/><br \/>\n<img decoding=\"async\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-114.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 114\" \/>= \\(\\frac{1}{6}\\).<br \/>\nExplanation:<br \/>\nGiven expression as \\(\\frac{4}{9}\\) X \\(\\frac{3}{8}\\),<br \/>\nStep I: We multiply the numerators as 4 X 3 = 12<br \/>\nStep II: We multiply denominators as 9 X 8 = 72<br \/>\nStep III: We write the fraction in the simplest form as \\(\\frac{12}{72}\\),<br \/>\nwe can further simplify as both goes in 12, 12 X 1 = 12 and 12 X 6 = 72, (1,6),<br \/>\nSo \\(\\frac{4}{9}\\) X \\(\\frac{3}{8}\\) = \\(\\frac{1}{6}\\).<\/p>\n<p>Question 4.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27190\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-115.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 115\" width=\"75\" height=\"53\" \/><br \/>\n<img decoding=\"async\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-115.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 115\" \/>= 16<\/p>\n<p>Explanation :<br \/>\n2\\(\\frac{2}{5}\\) X\u00a0 6\\(\\frac{2}{3}\\), We write mixed fractions<br \/>\n2\\(\\frac{2}{5}\\) as 2 X 5 +2 by 5 = \\(\\frac{12}{5}\\) and<br \/>\n6\\(\\frac{2}{3}\\) as 6 X 3 + 2 by 3 = \\(\\frac{20}{3}\\) Now we multiply<br \/>\n\\(\\frac{12}{5}\\) X \\(\\frac{20}{3}\\),<br \/>\nStep I: We multiply the numerators as 12 X 20 = 240<br \/>\nStep II: We multiply the denominators as 5 X 3 = 15<br \/>\nStep III: We write the fraction in the simplest form as \\(\\frac{240}{15}\\),<br \/>\nwe can further simplify as both goes in 15, 15 X 16 = 240 and 15 X 1 = 15, (16,1),<br \/>\ntherefore 2\\(\\frac{2}{5}\\) X\u00a0 6\\(\\frac{2}{3}\\) = 16.<\/p>\n<p><strong>Match the expression with its value.<\/strong><\/p>\n<p>Question 5.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27191\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-116.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 116\" width=\"92\" height=\"70\" \/><br \/>\n3 + 2 X 4<sup>2 <\/sup>= 35 matches with B<\/p>\n<p>Explanation:<br \/>\nGiven expression as 3 + 2 X 4<sup>2 <\/sup>= 3 + ( 2 X 4 X 4) = 3 + 32 = 35 which matches with B.<\/p>\n<p>Question 6.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27192\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-117.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 117\" width=\"104\" height=\"73\" \/><br \/>\n(3 + 2) X 4<sup>2 <\/sup>= 80 matches with D<\/p>\n<p>Explanation:<br \/>\nGiven expression as (3 + 2) X 4<sup>2 <\/sup>= 5 X (4 X 4) = 5 X 16 = 80 which matches with D.<\/p>\n<p>Question 7.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27193\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-118.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 118\" width=\"89\" height=\"75\" \/><\/p>\n<p>2 + 3 X 4<sup>2 <\/sup>= 50 matches with C<\/p>\n<p>Explanation:<br \/>\nGiven expression as 2 + 3 X 4<sup>2 <\/sup>= 2 + (3 X 4 X 4) = 2 + 48 = 50 which matches with C.<\/p>\n<p>Question 8.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27194\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-119.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 119\" width=\"92\" height=\"73\" \/><\/p>\n<p>4<sup>2 <\/sup>+ 2 X 3 = 22 matches with A<\/p>\n<p>Explanation:<br \/>\nGiven expression as 4<sup>2 <\/sup>+ 2 X 3 = 16 + 6 = 22 which matches with A.<\/p>\n<p><strong>Find the area of the rectangle.<\/strong><\/p>\n<p>Question 9.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27195\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-120.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 120\" width=\"133\" height=\"98\" \/><br \/>\nThe area of rectangle is 14 square feet<\/p>\n<p>Explanation:<br \/>\nGiven width as 4 ft and height as 3.5 ft, we can write 3.5 as \\(\\frac{35}{10}\\),<br \/>\nthe area of rectangle is 4 X \\(\\frac{35}{10}\\) = \\(\\frac{140}{10}\\)<br \/>\nas both goes in 10 we get \\(\\frac{140}{10}\\) =14 square feet.<\/p>\n<p>Question 10.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27196\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-121.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 121\" width=\"176\" height=\"92\" \/><br \/>\nThe area of rectangle is \\(\\frac{1}{6}\\) square feet<\/p>\n<p>Explanation:<br \/>\nGiven width as \\(\\frac{2}{3}\\) ft and height as \\(\\frac{1}{4}\\)<br \/>\nthe area of rectangle is \\(\\frac{2}{3}\\)\u00a0 X \\(\\frac{1}{4}\\)<br \/>\nStep I: We multiply the numerators as 2 X 1 = 2<br \/>\nStep II: We multiply the denominators as 3 X 4 = 12<br \/>\nStep III: We write the fraction in the simplest form as \\(\\frac{2}{12}\\),<br \/>\nwe can further simplify as both goes in 2, 2 X 1 = 2 and 2 X 6 = 12, (1,6),<br \/>\n\\(\\frac{1}{6}\\), therefore the area of rectangle is \\(\\frac{1}{6}\\) square feet.<\/p>\n<p>Question 11.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27197\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-122.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 122\" width=\"182\" height=\"103\" \/><br \/>\nThe area of rectangle is \\(\\frac{15}{16}\\) square yards<\/p>\n<p>Explanation:<br \/>\nGiven width as 1\\(\\frac{1}{2}\\) ft and height as \\(\\frac{5}{8}\\)<br \/>\nWe write mixed fractions 1\\(\\frac{1}{2}\\) as 1 X 2 +1 by 2 =<br \/>\n\\(\\frac{3}{2}\\) the area of rectangle is \\(\\frac{3}{2}\\)\u00a0 X \\(\\frac{5}{8}\\)<br \/>\nStep I: We multiply the numerators as 3 X 5 = 15<br \/>\nStep II: We multiply the denominators as 2 X 8 = 16<br \/>\nStep III: We write the fraction in the simplest form as \\(\\frac{15}{16}\\),<br \/>\ntherefore the area of rectangle is \\(\\frac{15}{16}\\) square yards.<\/p>\n<p><strong>Concepts, Skills, &amp; Problem Solving<\/strong><br \/>\n<strong>CHOOSE TOOLS<\/strong><br \/>\n<strong>Answer the question using a model.<\/strong> (See Exploration 1, p. 53.)<\/p>\n<p>Question 12.<br \/>\nHow many three-\ufb01fths are in three?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-50454\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-43-1.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-43\" width=\"565\" height=\"161\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-43-1.bmp 565w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-43-1-300x85.jpg 300w\" sizes=\"(max-width: 565px) 100vw, 565px\" \/><br \/>\nFive, three-\ufb01fths are in three<\/p>\n<p>Explanation:<br \/>\nGiven to find three-\ufb01fths are in three is three divides \\(\\frac{3}{5}\\)<br \/>\nwe write reciprocal of the fraction \\(\\frac{3}{5}\\) as \\(\\frac{5}{3}\\)=<br \/>\n3\u00a0 X \\(\\frac{5}{3}\\) = \\(\\frac{15}{3}\\) = 5.<\/p>\n<p>Question 13.<br \/>\nHow many two-ninths are in eight-ninths?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-50456\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-44.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-44\" width=\"1046\" height=\"274\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-44.bmp 1046w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-44-300x79.jpg 300w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-44-1024x268.jpg 1024w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-44-768x201.jpg 768w\" sizes=\"(max-width: 1046px) 100vw, 1046px\" \/><br \/>\nFour, two-ninths are in eight-ninths<\/p>\n<p>Explanation:<br \/>\nGiven to find two-ninths are in eight-ninths means \\(\\frac{8}{9}\\) \u00f7<br \/>\n\\(\\frac{2}{9}\\) we write reciprocal of the fraction \\(\\frac{2}{9}\\)<br \/>\nas \\(\\frac{9}{2}\\)= \\(\\frac{8}{9}\\) X \\(\\frac{9}{2}\\) =<br \/>\n\\(\\frac{8 X 9}{9 X 2}\\)= \\(\\frac{8}{2}\\) as both goes in 2<br \/>\nas 2 X 4 = 8, 2 X 1= 2,(4,1), \\(\\frac{8}{2}\\) = 4.<\/p>\n<p>Question 14.<br \/>\nHow many three-fourths are in seven-eighths?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-50597\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-45-1.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-45\" width=\"936\" height=\"254\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-45-1.bmp 936w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-45-1-300x81.jpg 300w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-45-1-768x208.jpg 768w\" sizes=\"(max-width: 936px) 100vw, 936px\" \/><br \/>\n\\(\\frac{7}{6}\\) or 1\\(\\frac{1}{6}\\), three-fourths are in seven-eighths<\/p>\n<p>Explanation:<br \/>\nGiven to find three-fourths are in seven-eighths means \\(\\frac{7}{8}\\) \u00f7<br \/>\n\\(\\frac{3}{4}\\) we write reciprocal of the fraction \\(\\frac{3}{4}\\) as \\(\\frac{4}{3}\\)= \\(\\frac{7}{8}\\) X \\(\\frac{4}{3}\\) =<br \/>\n\\(\\frac{7 X 4}{8 X 3}\\)= \\(\\frac{28}{24}\\) as both goes in 4<br \/>\nas 4 X 7 = 28, 4 X 6= 24,(7,6), \\(\\frac{7}{6}\\) as numerator is<br \/>\ngreater we write as ( 1 X 6 + 1 by 6) = 1\\(\\frac{1}{6}\\).<\/p>\n<p><strong>WRITING RECIPROCALS<\/strong><br \/>\n<strong>Write the reciprocal of the number.<\/strong><\/p>\n<p>Question 15.<br \/>\n8<br \/>\n8 the reciprocal is \\(\\frac{1}{8}\\)<\/p>\n<p>Explanation:<br \/>\nWe write the reciprocal of a number, \ufb01rst write the number as a fraction.<br \/>\nThen invert the fraction, so reciprocal of 8 is \\(\\frac{8}{1}\\) is \\(\\frac{1}{8}\\).<\/p>\n<p>Question 16.<br \/>\n\\(\\frac{6}{7}\\)<br \/>\n\\(\\frac{6}{7}\\) = \\(\\frac{7}{6}\\)<\/p>\n<p>Explanation:<br \/>\nAlready its in fraction so the reciprocal of \\(\\frac{6}{7}\\) is inverting the fraction<br \/>\n\\(\\frac{7}{6}\\).<\/p>\n<p>Question 17.<br \/>\n\\(\\frac{2}{5}\\)<br \/>\n\\(\\frac{2}{5}\\) = \\(\\frac{5}{2}\\)<\/p>\n<p>Explanation:<br \/>\nAlready its in fraction so the reciprocal of \\(\\frac{2}{5}\\) is inverting the fraction<br \/>\n\\(\\frac{5}{2}\\).<\/p>\n<p>Question 18.<br \/>\n\\(\\frac{11}{8}\\)<br \/>\n\\(\\frac{11}{8}\\) = \\(\\frac{8}{11}\\)<\/p>\n<p>Explanation:<br \/>\nAlready its in fraction so the reciprocal of \\(\\frac{11}{8}\\) is inverting the fraction<br \/>\n\\(\\frac{8}{11}\\).<\/p>\n<p><strong>DIVIDING FRACTIONS<\/strong><br \/>\n<strong>Divide. Write the answer in simplest form.<\/strong><\/p>\n<p>Question 19.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27198\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-123.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 123\" width=\"64\" height=\"56\" \/><br \/>\n<img decoding=\"async\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-123.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 123\" \/>= \\(\\frac{2}{3}\\)<br \/>\nExplanation:<br \/>\nGiven expressions as \\(\\frac{1}{3}\\) \u00f7 \\(\\frac{1}{2}\\)<br \/>\nwe write reciprocal of the fraction \\(\\frac{1}{2}\\) as \\(\\frac{2}{1}\\) and multiply as \\(\\frac{1}{3}\\) X \\(\\frac{2}{1}\\) =<br \/>\n\\(\\frac{1 X 2}{3 X 1}\\) = \\(\\frac{2}{3}\\),<br \/>\ntherefore \\(\\frac{1}{3}\\) \u00f7 \\(\\frac{1}{2}\\) = \\(\\frac{2}{3}\\).<\/p>\n<p>Question 20.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27199\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-124.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 124\" width=\"63\" height=\"52\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27199\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-124.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 124\" width=\"63\" height=\"52\" \/>= \\(\\frac{1}{2}\\)<br \/>\nExplanation:<br \/>\nGiven expressions as \\(\\frac{1}{8}\\) \u00f7 \\(\\frac{1}{4}\\)<br \/>\nwe write reciprocal of the fraction \\(\\frac{1}{4}\\) as<br \/>\n\\(\\frac{4}{1}\\) and multiply as \\(\\frac{1}{8}\\) X<br \/>\n\\(\\frac{4}{1}\\) = \\(\\frac{1 X 4}{8 X 1}\\) = \\(\\frac{4}{8}\\),<br \/>\nwe can further simplify as both goes in 4, 4 X 1 = 4 and 4 X 2 = 8, (1,2),<br \/>\ntherefore \\(\\frac{1}{8}\\) \u00f7 \\(\\frac{1}{4}\\) = \\(\\frac{1}{2}\\).<\/p>\n<p>Question 21.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27200\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-125.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 125\" width=\"52\" height=\"50\" \/><br \/>\n<img decoding=\"async\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-125.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 125\" \/>= \\(\\frac{1}{7}\\)<br \/>\nExplanation:<br \/>\nGiven expressions as \\(\\frac{2}{7}\\) \u00f7 2, we write reciprocal of 2 as<br \/>\n\\(\\frac{1}{2}\\) and multiply as \\(\\frac{2}{7}\\) X \\(\\frac{1}{2}\\) = \\(\\frac{2 X 1}{7 X 2}\\) = \\(\\frac{2}{14}\\),we can further<br \/>\nsimplify as both goes in 2, 2 X 1 = 2 and 2 X 7 = 14, (1,7), \\(\\frac{1}{7}\\),<br \/>\ntherefore \\(\\frac{2}{7}\\) \u00f7 2 = \\(\\frac{1}{7}\\).<\/p>\n<p>Question 22.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27201\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-126.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 126\" width=\"49\" height=\"44\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27201\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-126.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 126\" width=\"49\" height=\"44\" \/>= \\(\\frac{2}{5}\\)<br \/>\nExplanation:<br \/>\nGiven expressions as \\(\\frac{6}{5}\\) \u00f7 3, we write reciprocal of 3 as<br \/>\n\\(\\frac{1}{3}\\) and multiply as \\(\\frac{6}{5}\\) X<br \/>\n\\(\\frac{1}{3}\\) = \\(\\frac{6 X 1}{5 X 3}\\) = \\(\\frac{6}{15}\\),<br \/>\nwe can further simplify as both goes in 3, 3 X 2 = 6 and 3 X 5 = 15, (2,5),<br \/>\n\\(\\frac{2}{5}\\),therefore \\(\\frac{6}{5}\\) \u00f7 3 = \\(\\frac{2}{5}\\).<\/p>\n<p>Question 23.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27202\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-127.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 127\" width=\"60\" height=\"49\" \/><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-127.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 127\" \/>= \\(\\frac{3}{2}\\) = 1\\(\\frac{1}{2}\\)<br \/>\nExplanation:<br \/>\nGiven expressions as \\(\\frac{2}{3}\\) \u00f7 \\(\\frac{4}{9}\\),<br \/>\nwe write reciprocal of the fraction \\(\\frac{4}{9}\\) as \\(\\frac{9}{4}\\)<br \/>\nand multiply as \\(\\frac{2}{3}\\) X \\(\\frac{9}{4}\\) = \\(\\frac{2 X 9}{3 X 4}\\) = \\(\\frac{18}{12}\\),we can further simplify as both goes in 6,<br \/>\n6 X 3 = 18 and 6 X 2 = 12, (3,2),<br \/>\ntherefore \\(\\frac{2}{3}\\) \u00f7 \\(\\frac{4}{9}\\) = \\(\\frac{3}{2}\\) as numerator is greater than denominator we can write in mixed<br \/>\nfraction as (1 X 2 + 1 by 2) = 1\\(\\frac{1}{2}\\).<\/p>\n<p>Question 24.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27203\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-128.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 128\" width=\"68\" height=\"51\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27203\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-128.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 128\" width=\"68\" height=\"51\" \/>= \\(\\frac{35}{12}\\) = 2\\(\\frac{11}{12}\\)<br \/>\nExplanation:<br \/>\nGiven expressions as \\(\\frac{5}{6}\\) \u00f7 \\(\\frac{2}{7}\\),<br \/>\nwe write reciprocal of the fraction \\(\\frac{2}{7}\\) as \\(\\frac{7}{2}\\)<br \/>\nand multiply as \\(\\frac{5}{6}\\) X \\(\\frac{7}{2}\\) = \\(\\frac{5 X 7}{6 X 2}\\) = \\(\\frac{35}{12}\\),as numerator is greater than<br \/>\ndenominator we can write in mixed fraction as (2 X 12 + 11) by 12 =2\\(\\frac{11}{12}\\).Therefore \\(\\frac{5}{6}\\) \u00f7 \\(\\frac{2}{7}\\) = 2\\(\\frac{11}{12}\\).<\/p>\n<p>Question 25.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27204\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-129.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 129\" width=\"62\" height=\"48\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27204\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-129.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 129\" width=\"62\" height=\"48\" \/>= 16<br \/>\nExplanation:<br \/>\nGiven expressions as 12 \u00f7 \\(\\frac{3}{4}\\),<br \/>\nwe write reciprocal of the fraction \\(\\frac{3}{4}\\) as \\(\\frac{4}{3}\\)<br \/>\nand multiply as 12 X \\(\\frac{4}{3}\\) = \\(\\frac{12 X 4}{1 X 3}\\) =<br \/>\n\\(\\frac{48}{3}\\),we can further simplify as both goes in 3,<br \/>\n3 X 16 = 48 and 3 X 1 = 3, (16,1),therefore 12 \u00f7 \\(\\frac{3}{4}\\) = 16.<\/p>\n<p>Question 26.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27205\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-130.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 130\" width=\"55\" height=\"49\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27205\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-130.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 130\" width=\"55\" height=\"49\" \/>= 20<br \/>\nExplanation:<br \/>\nGiven expressions as 8 \u00f7 \\(\\frac{2}{5}\\), we write reciprocal of the fraction \\(\\frac{2}{5}\\) as \\(\\frac{5}{2}\\) and multiply as<br \/>\n8 X \\(\\frac{5}{2}\\) = \\(\\frac{8 X5}{1 X 2}\\) =<br \/>\n\\(\\frac{40}{2}\\),we can further simplify as both goes in 2,<br \/>\n2 X 20 = 40 and 2 X 1 = 2, (20,1),therefore 8 \u00f7 \\(\\frac{2}{5}\\) = 20.<\/p>\n<p>Question 27.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27206\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-131.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 131\" width=\"60\" height=\"48\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27206\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-131.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 131\" width=\"60\" height=\"48\" \/>= \\(\\frac{1}{14}\\)<br \/>\nExplanation:<br \/>\nGiven expressions as \\(\\frac{3}{7}\\) \u00f7 6, we write reciprocal of 6<br \/>\nas \\(\\frac{1}{6}\\) and multiply as \\(\\frac{3}{7}\\) X<br \/>\n\\(\\frac{1}{6}\\) = \\(\\frac{3 X 1}{7 X 6}\\) = \\(\\frac{3}{42}\\),<br \/>\nwe can further simplify as both goes in 3, 3 X 1 = 3 and 3 X 14 = 42, (1,14),<br \/>\ntherefore \\(\\frac{3}{7}\\) \u00f7 6 = \\(\\frac{1}{14}\\).<\/p>\n<p>Question 28.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27207\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-132.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 132\" width=\"67\" height=\"47\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27207\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-132.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 132\" width=\"67\" height=\"47\" \/>= \\(\\frac{3}{25}\\)<br \/>\nExplanation:<br \/>\nGiven expressions as \\(\\frac{12}{25}\\) \u00f7 4, we write reciprocal of 4<br \/>\nas \\(\\frac{1}{4}\\) and multiply as \\(\\frac{12}{25}\\) X \\(\\frac{1}{4}\\) = \\(\\frac{12 X 1}{25 X 4}\\) = \\(\\frac{12}{100}\\),<br \/>\nwe can further simplify as both goes in 4, 4 X 3 = 12 and 4 X 25 = 100, (3,25),<br \/>\ntherefore \\(\\frac{12}{25}\\) \u00f7 4 = \\(\\frac{3}{25}\\).<\/p>\n<p>Question 29.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27208\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-133.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 133\" width=\"54\" height=\"49\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27208\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-133.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 133\" width=\"54\" height=\"49\" \/>= \\(\\frac{1}{3}\\)<br \/>\nExplanation:<br \/>\nGiven expressions as \\(\\frac{2}{9}\\) \u00f7 \\(\\frac{2}{3}\\),<br \/>\nwe write reciprocal of the fraction \\(\\frac{2}{3}\\) as \\(\\frac{3}{2}\\)<br \/>\nand multiply as \\(\\frac{2}{9}\\) X \\(\\frac{3}{2}\\) = \\(\\frac{2 X 3}{9 X 2}\\) = \\(\\frac{6}{18}\\),we can further simplify as both goes in 6,<br \/>\n6 X 1 = 6 and 6 X 3 = 18, (1,3)= \\(\\frac{1}{3}\\).<br \/>\nTherefore \\(\\frac{2}{9}\\) \u00f7 \\(\\frac{2}{3}\\) = \\(\\frac{1}{3}\\).<\/p>\n<p>Question 30.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27209\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-134.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 134\" width=\"68\" height=\"56\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27209\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-134.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 134\" width=\"68\" height=\"56\" \/>= \\(\\frac{2}{3}\\)<br \/>\nExplanation:<br \/>\nGiven expressions as \\(\\frac{8}{15}\\) \u00f7 \\(\\frac{4}{5}\\),<br \/>\nwe write reciprocal of the fraction \\(\\frac{4}{5}\\) as \\(\\frac{5}{4}\\)<br \/>\nand multiply as \\(\\frac{8}{15}\\) X \\(\\frac{5}{4}\\) =<br \/>\n\\(\\frac{8 X 5}{15 X 4}\\) = \\(\\frac{40}{60}\\),<br \/>\nwe can further simplify as both goes in 20, 20 X 2 = 40 and<br \/>\n20 X 3 = 60, (2,3)=\\(\\frac{2}{3}\\).Therefore \\(\\frac{8}{15}\\) \u00f7<br \/>\n\\(\\frac{4}{5}\\) = \\(\\frac{2}{3}\\).<\/p>\n<p>Question 31.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27210\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-135.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 135\" width=\"53\" height=\"57\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27210\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-135.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 135\" width=\"53\" height=\"57\" \/>= 3<br \/>\nExplanation:<br \/>\nGiven expressions as \\(\\frac{1}{3}\\) \u00f7 \\(\\frac{1}{9}\\),<br \/>\nwe write reciprocal of the fraction \\(\\frac{1}{9}\\) as \\(\\frac{9}{1}\\)<br \/>\nand multiply as \\(\\frac{1}{3}\\) X \\(\\frac{9}{1}\\) =<br \/>\n\\(\\frac{1 X 9}{3 X 1}\\) = \\(\\frac{9}{3}\\),<br \/>\nwe can further simplify as both goes in 3, 3 X 3 = 9 and 3 X 1 = 3, (3,1)= 3.<br \/>\nTherefore \\(\\frac{1}{3}\\) \u00f7 \\(\\frac{1}{9}\\) = 3.<\/p>\n<p>Question 32.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27211\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-136.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 136\" width=\"62\" height=\"46\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27211\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-136.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 136\" width=\"62\" height=\"46\" \/>= \\(\\frac{28}{15}\\) = 1\\(\\frac{13}{15}\\)<br \/>\nExplanation:<br \/>\nGiven expressions as \\(\\frac{7}{10}\\) \u00f7 \\(\\frac{3}{8}\\),<br \/>\nwe write reciprocal of the fraction \\(\\frac{3}{8}\\) as \\(\\frac{8}{3}\\)<br \/>\nand multiply as \\(\\frac{7}{10}\\) X \\(\\frac{8}{3}\\) =<br \/>\n\\(\\frac{7 X 8}{10 X 3}\\) = \\(\\frac{56}{30}\\),<br \/>\nwe can further simplify as both goes in 2, 2 X 28 = 56 and 2 X 15 = 30,<br \/>\n(28,15)=\\(\\frac{28}{15}\\),as numerator is greater than<br \/>\ndenominator we can write in mixed fraction as (1 X 15 + 13 by 15) =<br \/>\n1\\(\\frac{13}{15}\\).Therefore \\(\\frac{7}{10}\\) \u00f7<br \/>\n\\(\\frac{3}{8}\\) = 1\\(\\frac{13}{15}\\).<\/p>\n<p>Question 33.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27212\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-137.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 137\" width=\"59\" height=\"47\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27212\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-137.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 137\" width=\"59\" height=\"47\" \/>= \\(\\frac{2}{27}\\)<br \/>\nExplanation:<br \/>\nGiven expressions as \\(\\frac{14}{27}\\) \u00f7 7,<br \/>\nwe write reciprocal of 7 as \\(\\frac{1}{7}\\) and multiply as<br \/>\n\\(\\frac{14}{27}\\) X \\(\\frac{1}{7}\\) = \\(\\frac{14 X 1}{27 X 7}\\) = \\(\\frac{14}{189}\\),we can further simplify as both goes in 7,<br \/>\n7 X 2 = 14 and 7 X 27 = 189, (2,27), \\(\\frac{2}{27}\\),therefore<br \/>\n\\(\\frac{14}{27}\\) \u00f7 7 = \\(\\frac{2}{27}\\).<\/p>\n<p>Question 34.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27213\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-138.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 138\" width=\"65\" height=\"50\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27213\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-138.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 138\" width=\"65\" height=\"50\" \/>= \\(\\frac{1}{24}\\)<br \/>\nExplanation:<br \/>\nGiven expressions as \\(\\frac{5}{8}\\) \u00f7 15, we write reciprocal of 15<br \/>\nas \\(\\frac{1}{15}\\) and multiply as \\(\\frac{5}{8}\\) X<br \/>\n\\(\\frac{1}{15}\\) = \\(\\frac{5 X 1}{8 X 15}\\) = \\(\\frac{5}{120}\\),<br \/>\nwe can further simplify as both goes in 5, 5 X 1 = 5 and 5 X 24 = 120, (1,24),<br \/>\n\\(\\frac{1}{24}\\),therefore \\(\\frac{5}{8}\\) \u00f7 15<br \/>\n= \\(\\frac{1}{24}\\).<\/p>\n<p>Question 35.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27214\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-139.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 139\" width=\"64\" height=\"49\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27214\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-139.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 139\" width=\"64\" height=\"49\" \/>= \\(\\frac{27}{28}\\)<br \/>\nExplanation:<br \/>\nGiven expressions as \\(\\frac{27}{32}\\) \u00f7 \\(\\frac{7}{8}\\),<br \/>\nwe write reciprocal of the fraction \\(\\frac{7}{8}\\) as \\(\\frac{8}{7}\\)<br \/>\nand multiply as \\(\\frac{27}{32}\\) X \\(\\frac{8}{7}\\) =<br \/>\n\\(\\frac{27 X 8}{32 X 7}\\) = \\(\\frac{216}{224}\\),<br \/>\nwe can further simplify as both goes in 8, 8 X 27 = 216 and 8 X 28 = 224,<br \/>\n(27,28)=\\(\\frac{27}{28}\\).Therefore \\(\\frac{27}{32}\\) \u00f7<br \/>\n\\(\\frac{7}{8}\\) = \\(\\frac{27}{28}\\).<\/p>\n<p>Question 36.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27215\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-140.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 140\" width=\"73\" height=\"47\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27215\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-140.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 140\" width=\"73\" height=\"47\" \/>= \\(\\frac{26}{75}\\)<br \/>\nExplanation:<br \/>\nGiven expressions as \\(\\frac{4}{15}\\) \u00f7 \\(\\frac{10}{13}\\),<br \/>\nwe write reciprocal of the fraction \\(\\frac{10}{13}\\) as<br \/>\n\\(\\frac{13}{10}\\) and multiply as \\(\\frac{4}{15}\\) X<br \/>\n\\(\\frac{13}{10}\\) = \\(\\frac{4 X 13}{15 X 10}\\) =<br \/>\n\\(\\frac{52}{150}\\),we can further simplify as both goes in 2,<br \/>\n2 X 26 = 52 and 2 X 75 = 150, (26,75)=\\(\\frac{26}{75}\\).<br \/>\nTherefore \\(\\frac{4}{15}\\) \u00f7 \\(\\frac{10}{13}\\) = \\(\\frac{26}{75}\\).<\/p>\n<p>Question 37.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27216\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-141.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 141\" width=\"61\" height=\"58\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27216\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-141.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 141\" width=\"61\" height=\"58\" \/>= \\(\\frac{81}{4}\\) = 20\\(\\frac{1}{4}\\)<br \/>\nExplanation:<br \/>\nGiven expressions as 9 \u00f7 \\(\\frac{4}{9}\\), we write reciprocal of<br \/>\nthe fraction \\(\\frac{4}{9}\\) as \\(\\frac{9}{4}\\)<br \/>\nand multiply as 9 X \\(\\frac{9}{4}\\) = \\(\\frac{9 X 9}{1 X 4}\\) =<br \/>\n\\(\\frac{81}{4}\\),as numerator is greater than denominator<br \/>\nwe can write in mixed fraction as (20 X 4 + 1 by 4) = 20\\(\\frac{1}{4}\\),<br \/>\ntherefore 9 \u00f7 \\(\\frac{4}{9}\\) = 20\\(\\frac{1}{4}\\).<\/p>\n<p>Question 38.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27217\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-142.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 142\" width=\"75\" height=\"53\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27217\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-142.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 142\" width=\"75\" height=\"53\" \/>= 24<br \/>\nExplanation:<br \/>\nGiven expressions as 10 \u00f7 \\(\\frac{5}{12}\\), we write reciprocal<br \/>\nof the fraction \\(\\frac{5}{12}\\) as \\(\\frac{12}{5}\\) and<br \/>\nmultiply as 10 X \\(\\frac{12}{5}\\) = \\(\\frac{10 X 12}{1 X 5}\\) =<br \/>\n\\(\\frac{120}{5}\\),we can further simplify as both goes in 5,<br \/>\n5 X 24 = 120 and 5 X 1 = 5, (24,1)= 24.Therefore 10 \u00f7 \\(\\frac{5}{12}\\) = 24.<\/p>\n<p><strong>YOU BE THE TEACHER<\/strong><br \/>\n<strong>Your friend \ufb01nds the quotient. Is your friend correct? Explain your reasoning.<\/strong><\/p>\n<p>Question 39.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27218\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-143.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 143\" width=\"207\" height=\"163\" \/><\/p>\n<p>Yes, friend is correct as \\(\\frac{4}{7}\\) \u00f7 \\(\\frac{13}{28}\\) =<br \/>\n1\\(\\frac{3}{13}\\).<\/p>\n<p>Explanation:<br \/>\nGiven expression as \\(\\frac{4}{7}\\) \u00f7 \\(\\frac{13}{28}\\),<br \/>\nwe write reciprocal of the fraction \\(\\frac{13}{28}\\) as<br \/>\n\\(\\frac{28}{13}\\) and multiply as \\(\\frac{4}{7}\\) X<br \/>\n\\(\\frac{28}{13}\\) = \\(\\frac{4 X 28}{7 X 13}\\) = \\(\\frac{112}{91}\\),<br \/>\nwe can further simplify as both goes in 7, 7 X 16 = 112 and 7 X 13 = 91,<br \/>\n(16,13) = \\(\\frac{16}{13}\\), as numerator is greater than denominator<br \/>\nwe can write in mixed fraction as (1 X 13 + 3 by 13) = 1\\(\\frac{3}{13}\\).<br \/>\nTherefore \\(\\frac{4}{7}\\) \u00f7 \\(\\frac{13}{28}\\) = 1\\(\\frac{3}{13}\\).<br \/>\nSo friend is correct.<\/p>\n<p>Question 40.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27219\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-144.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 144\" width=\"186\" height=\"177\" \/><br \/>\nNo, Friend is incorrect as \\(\\frac{2}{5}\\) \u00f7 \\(\\frac{8}{9}\\) =<br \/>\n\\(\\frac{9}{20}\\) \u2260 2\\(\\frac{2}{9}\\)<\/p>\n<p>Explanation:<br \/>\nGiven expression as \\(\\frac{2}{5}\\) \u00f7 \\(\\frac{8}{9}\\),<br \/>\nwe write reciprocal of the fraction \\(\\frac{8}{9}\\) as<br \/>\n\\(\\frac{9}{8}\\) and multiply as \\(\\frac{2}{5}\\) X<br \/>\n\\(\\frac{9}{8}\\) = \\(\\frac{2 X 9}{5 X 8}\\) = \\(\\frac{18}{40}\\),<br \/>\nwe can further simplify as both goes in 2, 2 X 9 = 18 and 2 X 20 = 40,<br \/>\n(9,20) = \\(\\frac{9}{20}\\).Therefore \\(\\frac{2}{5}\\) \u00f7<br \/>\n\\(\\frac{8}{9}\\) = \\(\\frac{9}{20}\\).<br \/>\nNo, Friend is incorrect as \\(\\frac{2}{5}\\) \u00f7 \\(\\frac{8}{9}\\) =<br \/>\n\\(\\frac{9}{20}\\) \u2260 2\\(\\frac{2}{9}\\).<\/p>\n<p>Question 41.<br \/>\n<strong>REASONING<\/strong><br \/>\nYou have \\(\\frac{3}{5}\\) of an apple pie. You divide the remaining pie into 5 equal slices. What portion of the original pie is each slice?<\/p>\n<p>\\(\\frac{3}{25}\\) of the original pie is each slice<\/p>\n<p>Explanation:<br \/>\nGiven I have \\(\\frac{3}{5}\\) of an apple pie and divide<br \/>\nthe remaining pie into 5 equal slices. So the portion of the original pie<br \/>\nin each slice is \\(\\frac{3}{5}\\) \u00f7\u00a0 5 we write reciprocal of 5<br \/>\nas \\(\\frac{1}{5}\\) and multiply as \\(\\frac{3}{5}\\) X<br \/>\n\\(\\frac{1}{5}\\) = \\(\\frac{3 X 1}{5 X 5}\\) = \\(\\frac{3}{25}\\),<br \/>\ntherefore \\(\\frac{3}{25}\\) of the original pie is each slice.<\/p>\n<p>Question 42.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nHow many times longer is the baby alligator than the baby gecko?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27220\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-145.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 145\" width=\"735\" height=\"162\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-145.png 735w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-145-300x66.png 300w\" sizes=\"(max-width: 735px) 100vw, 735px\" \/><br \/>\n5\\(\\frac{5}{8}\\) times longer is the baby alligator than the baby gecko<\/p>\n<p>Explanation:<br \/>\nGiven baby alligator is \\(\\frac{3}{4}\\) long and baby gecko<br \/>\nis \\(\\frac{2}{15}\\), So baby alligator is more long than the<br \/>\nbaby gecko by \\(\\frac{3}{4}\\) \u00f7 \\(\\frac{2}{15}\\),<br \/>\nwe write reciprocal of the fraction \\(\\frac{2}{15}\\) as<br \/>\n\\(\\frac{15}{2}\\) and multiply as \\(\\frac{3}{4}\\) X<br \/>\n\\(\\frac{15}{2}\\) = \\(\\frac{3 X 15}{4 X 2}\\) =<br \/>\n\\(\\frac{45}{8}\\),as numerator is greater than denominator<br \/>\nwe can write in mixed fraction as (5 X 8 + 5 by 8) = 5\\(\\frac{5}{8}\\).<br \/>\nTherefore 5\\(\\frac{5}{8}\\) times longer is the baby alligator<br \/>\nthan the baby gecko.<\/p>\n<p><strong>OPEN-ENDED<\/strong><br \/>\n<strong>Write a real-life problem for the expression. Then solve the problem.<\/strong><\/p>\n<p>Question 43.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27221\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-146.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 146\" width=\"58\" height=\"49\" \/><br \/>\nThe rope of length \\(\\frac{5}{6}\\)cm is cut into 4 equal pieces,<br \/>\nhow long is each piece?<br \/>\n\\(\\frac{5}{24}\\) cm long is each piece<\/p>\n<p>Explanation:<br \/>\nWrote a real -life problem, the rope of length \\(\\frac{5}{6}\\)cm<br \/>\nis cut into 4 equal pieces, how long is each piece and solution is<br \/>\n\\(\\frac{5}{6}\\)\u00f7 4,we write reciprocal of 4 as \\(\\frac{1}{4}\\)<br \/>\nand multiply as \\(\\frac{5}{6}\\) X \\(\\frac{1}{4}\\) =<br \/>\n\\(\\frac{5 X 1}{4 X 6}\\) = \\(\\frac{5}{24}\\),<br \/>\ntherefore each piece is of length \\(\\frac{5}{24}\\) cm long is each piece.<\/p>\n<p>Question 44.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27222\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-147.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 147\" width=\"57\" height=\"51\" \/><br \/>\nA jug contains \\(\\frac{2}{5}\\) of orange juice,<br \/>\nI drank \\(\\frac{3}{8}\\) portion<br \/>\nin it, So how much portion of juice I drank?<br \/>\nSo I drank 1\\(\\frac{1}{15}\\) portion of orange juice.<\/p>\n<p>Explanation:<br \/>\nWrote a real -life problem, a jug contains \\(\\frac{2}{5}\\) of<br \/>\norange juice, I drank \\(\\frac{3}{8}\\) portion in it,<br \/>\nSo portion of juice I drank is \\(\\frac{5}{6}\\) \u00f7 \\(\\frac{3}{8}\\)<br \/>\nwe write reciprocal of fraction \\(\\frac{3}{8}\\) as<br \/>\n\\(\\frac{8}{3}\\) and multiply as \\(\\frac{2}{5}\\) X<br \/>\n\\(\\frac{8}{3}\\) = \\(\\frac{2 X 8}{5 X 3}\\) =<br \/>\n\\(\\frac{16}{15}\\),as numerator is greater than denominator<br \/>\nwe can write in mixed fraction as (1 X 15 + 1 by 15) = 1\\(\\frac{1}{15}\\),<br \/>\nSo I drank 1\\(\\frac{1}{15}\\) portion of orange juice.<\/p>\n<p>Question 45.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27223\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-148.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 148\" width=\"61\" height=\"48\" \/><\/p>\n<p>I need \\(\\frac{2}{3}\\)ltrs of milk to feed one dog,<br \/>\nHow many dogs I do can feed in 10 ltrs of milk.<br \/>\nI can feed 15 dogs.<\/p>\n<p>Explanation:<br \/>\nWrote a real -life problem,I need \\(\\frac{2}{3}\\)ltrs of<br \/>\nmilk to feed one dog, How many dogs I do can feed in 10 ltrs of milk.<br \/>\nSo number of dogs I can feed are 10 \u00f7 \\(\\frac{2}{3}\\)<br \/>\nwe write reciprocal of fraction \\(\\frac{2}{3}\\) as \\(\\frac{3}{2}\\)<br \/>\nand multiply as 10 X \\(\\frac{3}{2}\\) = \\(\\frac{30}{2}\\) as<br \/>\nboth goes in 2, 2 x 15 = 30 and 2 x 1 = 2,(15,1),So \\(\\frac{30}{2}\\)=15,<br \/>\nSo I can feed 15 dogs.<\/p>\n<p>Question 46.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27224\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-149.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 149\" width=\"50\" height=\"50\" \/><br \/>\nIn a class there are \\(\\frac{2}{7}\\) girls in that \\(\\frac{4}{9}\\)<br \/>\nlike playing chess, how many girls like playing chess ?<br \/>\nThere are \\(\\frac{9}{14}\\) girls like playing chess in a class<\/p>\n<p>Explanation:<br \/>\nWrote a real -life problem, In a class there are \\(\\frac{2}{7}\\)<br \/>\ngirls in that \\(\\frac{4}{9}\\) like playing chess, how many girls like<br \/>\nplaying chess so \\(\\frac{2}{7}\\) \u00f7 \\(\\frac{4}{9}\\),<br \/>\nwe write reciprocal of fraction \\(\\frac{4}{9}\\) as \\(\\frac{9}{4}\\)<br \/>\nand multiply as \\(\\frac{2}{7}\\) X \\(\\frac{9}{4}\\) = \\(\\frac{2 X 9}{7 X 4}\\)= \\(\\frac{18}{28}\\) we can further simplify<br \/>\nas both goes 2, 2 X 9 = 18, 2 X 14 = 28,(9,14)= \\(\\frac{9}{14}\\)<br \/>\ngirls like playing chess in a class.<\/p>\n<p><strong>NUMBER SENSE<\/strong><br \/>\n<strong>Copy and complete the statement.<\/strong><\/p>\n<p>Question 47.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27225\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-150.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 150\" width=\"111\" height=\"56\" \/><br \/>\nThe statement is \\(\\frac{5}{12}\\) X \\(\\frac{12}{5}\\) = 1.<\/p>\n<p>Explanation:<br \/>\nLets take the missing number as x, \\(\\frac{5}{12}\\) X x = 1,<br \/>\ntherefore when \\(\\frac{5}{12}\\) goes other side it becomes<br \/>\nreciprocal, So x= 1 X \\(\\frac{12}{5}\\), The statement is<br \/>\n\\(\\frac{5}{12}\\) X \\(\\frac{12}{5}\\) = 1.<\/p>\n<p>Question 48.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27226\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-151.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 151\" width=\"102\" height=\"42\" \/><br \/>\nThe statement is 3 X \\(\\frac{1}{3}\\) = 1.<\/p>\n<p>Explanation:<br \/>\nLets take the missing number as x, 3 X x = 1,therefore<br \/>\nwhen 3 goes other side it becomes reciprocal as<br \/>\n\\(\\frac{1}{3}\\), So x= 1 X \\(\\frac{1}{3}\\),<br \/>\nThe statement is 3 X \\(\\frac{1}{3}\\) = 1.<\/p>\n<p>Question 49.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27227\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-152.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 152\" width=\"115\" height=\"51\" \/><br \/>\n7 \u00f7 \\(\\frac{1}{8}\\) = 56<\/p>\n<p>Explanation:<br \/>\nLets take the missing number as x, So 7 \u00f7 x = 56 , x = 7\u00f756 =<br \/>\n7 X \\(\\frac{1}{56}\\)\\(\\frac{7}{56}\\) as both goes in 7,<br \/>\n7 X 1 = 7, 7 X 8 = 56,(1,8) = \\(\\frac{1}{8}\\),<br \/>\nx =\\(\\frac{1}{8}\\), The statement is\u00a0 7 \u00f7 \\(\\frac{1}{8}\\) = 56.<\/p>\n<p><strong>REASONING<\/strong><br \/>\n<strong>Without \ufb01nding the quotient, copy and complete the statement using &lt;, &gt;, or =. Explain your reasoning.<\/strong><\/p>\n<p>Question 50.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27228\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-153.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 153\" width=\"97\" height=\"46\" \/><br \/>\nIs &lt;<br \/>\n\\(\\frac{7}{9}\\) \u00f7 5 &lt; \\(\\frac{7}{9}\\)<\/p>\n<p>Explanation:<br \/>\nL.H.S is \\(\\frac{7}{9}\\) \u00f7 5\u00a0 and R.H.S is \\(\\frac{7}{9}\\)<br \/>\nwhen compared both sides we have \\(\\frac{7}{9}\\) and<br \/>\nL.H.S is still 1 divided by 5 so it becomes less than R.H.S 1.<br \/>\nSo \\(\\frac{7}{9}\\) \u00f7 5 &lt; \\(\\frac{7}{9}\\).<\/p>\n<p>Question 51.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27229\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-154.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 154\" width=\"100\" height=\"53\" \/><br \/>\nIs =<br \/>\n\\(\\frac{3}{7}\\) \u00f7 1 = \\(\\frac{3}{7}\\)<br \/>\nExplanation:<br \/>\nL.H.S is \\(\\frac{3}{7}\\) \u00f7 1\u00a0 and R.H.S is \\(\\frac{3}{7}\\)<br \/>\nwhen compared both sides we have \\(\\frac{3}{7}\\) and<br \/>\nL.H.S is still 1 divided by 1 so it becomes equal to R.H.S 1.<br \/>\nSo \\(\\frac{3}{7}\\) \u00f7 1 &lt; \\(\\frac{3}{7}\\).<\/p>\n<p>Question 52.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27230\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-155.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 155\" width=\"95\" height=\"53\" \/><br \/>\nIs &gt;<br \/>\n8 \u00f7 \\(\\frac{3}{4}\\) &gt; 8<\/p>\n<p>Explanation:<br \/>\nL.H.S is 8 \u00f7 \\(\\frac{3}{4}\\)\u00a0 and R.H.S is 8 when compared<br \/>\nboth sides we have 8 and L.H.S is still 3 divided by 4 so it becomes<br \/>\n1 \u00f7 \\(\\frac{3}{4}\\) ,we write reciprocal of\u00a0 \\(\\frac{3}{4}\\) as<br \/>\n\\(\\frac{4}{3}\\) ,1 X \\(\\frac{4}{3}\\) now numerator is<br \/>\ngreater than denominator, we get 1 whole plus number in L.H.S,<br \/>\nas L.H.S is greater than R.H.S 1. So 8 \u00f7 \\(\\frac{3}{4}\\) &gt; 8.<\/p>\n<p>Question 53.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27231\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-156.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 156\" width=\"107\" height=\"51\" \/><\/p>\n<p>Is &gt;<br \/>\n\\(\\frac{5}{6}\\) \u00f7 \\(\\frac{7}{8}\\) &gt; \\(\\frac{5}{6}\\)<\/p>\n<p>Explanation:<br \/>\nL.H.S is \\(\\frac{5}{6}\\) \u00f7 \\(\\frac{7}{8}\\)\u00a0 and<br \/>\nR.H.S is \\(\\frac{5}{6}\\) when compared both sides we<br \/>\nhave \\(\\frac{5}{6}\\) and L.H.S is still 7 divided by 8 so it<br \/>\nbecomes 1 \u00f7 \\(\\frac{7}{8}\\)\u00a0 we write reciprocal of<br \/>\n\\(\\frac{7}{8}\\) as\u00a0 \\(\\frac{8}{7}\\)= 1 X \\(\\frac{8}{7}\\)<br \/>\nnow numerator is greater than denominator, so we get 1 whole plus<br \/>\nnumber in L.H.S as L.H.S is greater than R.H.S 1.<br \/>\nSo \\(\\frac{5}{6}\\) \u00f7 \\(\\frac{7}{8}\\) &gt; \\(\\frac{5}{6}\\).<\/p>\n<p><strong>ORDER OF OPERATIONS<\/strong><br \/>\n<strong>Evaluate the expression. Write the answer in simplest form.<\/strong><\/p>\n<p>Question 54.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27232\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-157.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 157\" width=\"87\" height=\"51\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27232\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-157.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 157\" width=\"87\" height=\"51\" \/>= \\(\\frac{1}{6}\\)<br \/>\nExplanation:<br \/>\nGiven expression as \\(\\frac{1}{6}\\) \u00f7 6 \u00f7 6, first<br \/>\nwe write as multiplication as \\(\\frac{1}{6}\\) \u00f7 (6 X \\(\\frac{1}{6}\\)) = \\(\\frac{1}{6}\\) \u00f7 1 = \\(\\frac{1}{6}\\).<\/p>\n<p>Question 55.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27233\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-158.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 158\" width=\"104\" height=\"52\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27233\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-158.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 158\" width=\"104\" height=\"52\" \/>= \\(\\frac{1}{144}\\)<br \/>\nExplanation:<br \/>\nGiven expression as \\(\\frac{7}{12}\\) \u00f7 14 \u00f7 6,14<br \/>\nand 6 becomes reciprocals and multiplied as \\(\\frac{7}{12}\\) X<br \/>\n\\(\\frac{1}{14}\\) X \\(\\frac{1}{6}\\)<br \/>\n= \\(\\frac{7 X 1 X 1 }{12 X 14 X 6 }\\) =\u00a0 \\(\\frac{7}{1008}\\),<br \/>\nwe now further simplify as both goes in 7, 7 X 1 = 7, 7 X 144 = 1008,<br \/>\n(1, 144) = \\(\\frac{1}{144}\\).<\/p>\n<p>Question 56.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27234\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-159.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 159\" width=\"93\" height=\"45\" \/><br \/>\n\\(\\frac{3}{5}\\) \u00f7 \\(\\frac{4}{7}\\) \u00f7 \\(\\frac{9}{10}\\) = \\(\\frac{7}{6}\\)<br \/>\nExplanation:<br \/>\nGiven expression as \\(\\frac{3}{5}\\) \u00f7 \\(\\frac{4}{7}\\) \u00f7<br \/>\n\\(\\frac{9}{10}\\) ,\\(\\frac{4}{7}\\),\\(\\frac{9}{10}\\)<br \/>\nbecomes reciprocals and been multipled as = \\(\\frac{3}{5}\\) X<br \/>\n\\(\\frac{7}{4}\\) X \\(\\frac{10}{9}\\)=<br \/>\n\\(\\frac{3 X 7 X 10}{5 X 4 X 9}\\) = \\(\\frac{210}{180}\\)<br \/>\nwe can further simplify as both goes in 30,<br \/>\n30 X 7 = 210, 30 X 6 = 180,(7,6) = \\(\\frac{7}{6}\\),therefore<br \/>\n\\(\\frac{3}{5}\\) \u00f7 \\(\\frac{4}{7}\\) \u00f7 \\(\\frac{9}{10}\\) =<br \/>\n\\(\\frac{7}{6}\\).<\/p>\n<p>Question 57.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27235\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-160.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 160\" width=\"84\" height=\"55\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27235\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-160.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 160\" width=\"84\" height=\"55\" \/>= 4<br \/>\nExplanation:<br \/>\nGiven expression as 4 \u00f7 \\(\\frac{8}{9}\\) &#8211; \\(\\frac{1}{2}\\) ,<br \/>\nfirst we calculate 4 \u00f7 \\(\\frac{8}{9}\\) we write \\(\\frac{8}{9}\\)<br \/>\nas reciprocal \\(\\frac{9}{8}\\) and multiply with 4 as<br \/>\n4 X \\(\\frac{9}{8}\\) = \\(\\frac{4 x 9}{8}\\) =<br \/>\n\\(\\frac{36}{8}\\) we simplifies as both goes in 4 as 4 X 9 = 36,<br \/>\n4 x 2 = 8, (9,2) = \\(\\frac{9}{2}\\) now we subtract \\(\\frac{1}{2}\\)<br \/>\nas both denominators are 2 we subtract numerators as (9 -1)= 8,<br \/>\nwe get \\(\\frac{8}{2}\\) = 4.<\/p>\n<p>Question 58.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27236\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-161.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 161\" width=\"87\" height=\"58\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27236\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-161.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 161\" width=\"87\" height=\"58\" \/>= 2<br \/>\nExplanation:<br \/>\nGiven expression as \\(\\frac{3}{4}\\) + \\(\\frac{5}{6}\\) \u00f7<br \/>\n\\(\\frac{2}{3}\\), first we calculate \\(\\frac{5}{6}\\) \u00f7<br \/>\n\\(\\frac{2}{3}\\) we write \\(\\frac{2}{3}\\) reciprocal and<br \/>\nmultiply as \\(\\frac{5}{6}\\) X \\(\\frac{3}{2}\\) =<br \/>\n\\(\\frac{5 X 3}{6 X 2}\\) =\\(\\frac{15}{12}\\)<br \/>\nwe simplify further as both goes in 3, 3 X 5 = 15, 3 X 4 = 12, (5,4)=<br \/>\n\\(\\frac{5}{4}\\) now we add with \\(\\frac{3}{4}\\) ,<br \/>\n\\(\\frac{3}{4}\\) + \\(\\frac{5}{4}\\) as both have same<br \/>\ndenominator we add numerators as 3 + 5 = 8 and write as<br \/>\n\\(\\frac{8}{4}\\) as both goes in 4,we get 2.<br \/>\nTherefore \\(\\frac{3}{4}\\) + \\(\\frac{5}{6}\\) \u00f7<br \/>\n\\(\\frac{2}{3}\\) = 2.<\/p>\n<p>Question 59.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27237\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-162.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 162\" width=\"79\" height=\"51\" \/><\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27237\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-162.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 162\" width=\"79\" height=\"51\" \/>= \\(\\frac{5}{6}\\)<br \/>\nExplanation:<br \/>\nGiven expression as \\(\\frac{7}{8}\\) &#8211; \\(\\frac{3}{8}\\) \u00f7 9 ,<br \/>\nfirst we calculate \\(\\frac{3}{8}\\) \u00f7 9,now we write 9 reciprocal and multiply as \\(\\frac{3}{8}\\) X \\(\\frac{1}{9}\\) = \\(\\frac{3 X 1}{8 X 9}\\) =\\(\\frac{3}{72}\\) \u00a0we can simplify as both goes in 3,<br \/>\n3 X 1 =3, 3 X 24 =72, (1,24) = \\(\\frac{1}{24}\\)\u00a0 now we subtract from<br \/>\n\\(\\frac{7}{8}\\) &#8211; \\(\\frac{1}{24}\\) as we need both<br \/>\nto have same denominators 24 we multiply \\(\\frac{7}{8}\\) X<br \/>\n\\(\\frac{3}{3}\\) = \\(\\frac{7 X 3}{8 X 3}\\) =\\(\\frac{21}{24}\\),<br \/>\nNow \\(\\frac{21}{24}\\) &#8211; \\(\\frac{1}{24}\\)<br \/>\nas both have same 24 denominators now we can subtract<br \/>\nnumerators as 21 &#8211; 1 = 20 and write as \\(\\frac{20}{24}\\)<br \/>\nas both goes in 4, 4 X 5 = 20, 4 X 6 = 24, (5, 6) = \\(\\frac{5}{6}\\),<br \/>\nTherefore \\(\\frac{7}{8}\\) &#8211; \\(\\frac{3}{8}\\) \u00f7 9 = \\(\\frac{5}{6}\\).<\/p>\n<p>Question 60.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27238\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-163.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 163\" width=\"93\" height=\"50\" \/><br \/>\n<img decoding=\"async\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-163.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 163\" \/>= 4 \\(\\frac{7}{8}\\)<br \/>\nExplanation:<br \/>\nGiven expression as \\(\\frac{9}{16}\\) \u00f7 \\(\\frac{3}{4}\\) X<br \/>\n\\(\\frac{2}{13}\\), first we calculate \\(\\frac{3}{4}\\) X<br \/>\n\\(\\frac{2}{13}\\) = \\(\\frac{3 X 2}{4 X 13}\\) = \\(\\frac{6}{52}\\)<br \/>\nwe can simplify as both goes in 2, 2 X 3 =6, 2 X 26 = 52, (3, 26) =<br \/>\n\\(\\frac{3}{26}\\) now\u00a0 \\(\\frac{9}{16}\\) \u00f7 \\(\\frac{3}{26}\\)<br \/>\nwe write reciprocal and multiply \\(\\frac{9}{16}\\) X<br \/>\n\\(\\frac{26}{3}\\) = \\(\\frac{9 x 26}{16 X 3}\\) =<br \/>\n\\(\\frac{234}{48}\\) as both can go in 6, 6 X 39 = 234<br \/>\nand 6 X 8 = 48, (39,8) = \\(\\frac{234}{48}\\) = \\(\\frac{39}{8}\\)<br \/>\nas numerator is greater than denominator we can write as (4 X 8 + 7 by 8)\u00a0 =<br \/>\n4\\(\\frac{7}{8}\\).<\/p>\n<p>Question 61.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27149\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-164.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 164\" width=\"91\" height=\"54\" \/><\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27149\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-164.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 164\" width=\"91\" height=\"54\" \/>= \\(\\frac{1}{10}\\)<\/p>\n<p>Explanation:<br \/>\nGiven expression as \\(\\frac{3}{14}\\) X \\(\\frac{2}{5}\\) \u00f7<br \/>\n\\(\\frac{6}{7}\\), We write \\(\\frac{6}{7}\\) as<br \/>\nreciprocal \\(\\frac{7}{6}\\) and multiply as \\(\\frac{3}{14}\\)<br \/>\nX \\(\\frac{2}{5}\\) X \\(\\frac{7}{6}\\)=<br \/>\n\\(\\frac{3 X 2 X 7}{14 X 5 X 6}\\) = \\(\\frac{42}{420}\\)<br \/>\nas both goes in 42, 42 X 1= 42 and 42 X 10 = 420, (1, 10) =<br \/>\n\\(\\frac{1}{10}\\), therefore \\(\\frac{3}{14}\\) X<br \/>\n\\(\\frac{2}{5}\\) \u00f7 \\(\\frac{6}{7}\\) = \\(\\frac{1}{10}\\).<\/p>\n<p>Question 62.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27150\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-165.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 165\" width=\"103\" height=\"57\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27150\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-165.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 165\" width=\"103\" height=\"57\" \/>= \\(\\frac{2}{3}\\)<br \/>\nExplanation:<br \/>\nGiven expression as \\(\\frac{10}{27}\\) X (\\(\\frac{3}{8}\\) \u00f7<br \/>\n\\(\\frac{5}{24}\\)), first we calculate \\(\\frac{3}{8}\\) \u00f7<br \/>\n\\(\\frac{5}{24}\\), we write\u00a0 \\(\\frac{5}{24}\\) reciprocal<br \/>\nas \\(\\frac{24}{5}\\) and multiply as \\(\\frac{3}{8}\\) X<br \/>\n\\(\\frac{24}{5}\\) = \\(\\frac{3 X 24}{8 X 5}\\) = \\(\\frac{72}{40}\\),<br \/>\nwe can simplify as both goes in 8 as 8 x 9 = 72 and<br \/>\n8 X 5 = 40, (9,5) = \\(\\frac{9}{5}\\), now we multiply<br \/>\n\\(\\frac{10}{27}\\) X \\(\\frac{9}{5}\\) =<br \/>\n\\(\\frac{10 X 9}{27 X 5}\\) = \\(\\frac{90}{135}\\)<br \/>\nwe can further simplify as both goes in 45, 45 X 2 = 90,<br \/>\n45 x 3 = 135, (2, 3) = \\(\\frac{2}{3}\\).<\/p>\n<p>Question 63.<br \/>\n<strong>NUMBER SENSE<\/strong><br \/>\nWhen is the reciprocal of a fraction a whole number? Explain.<\/p>\n<p><span id=\"P523_524\" class=\"s1 f1699 fs0 l0\">When the simpli\ufb01<\/span><span id=\"P523_526\" class=\"s1 f1699 fs0 l0\">ed fraction has a 1 in the <\/span><span id=\"P523_527\" class=\"s1 f1699 fs0 l0\">numerator,<br \/>\nTh<\/span><span id=\"P523_529\" class=\"s1 f1699 fs0 l0\">e reciprocal will have a 1 in the <\/span><span id=\"P523_530\" class=\"s1 f1699 fs0 l0\">denominator. We get a whole number<\/span><\/p>\n<p>Explanation:<br \/>\n<span id=\"P523_524\" class=\"s1 f1699 fs0 l0\">When the simpli\ufb01<\/span><span id=\"P523_526\" class=\"s1 f1699 fs0 l0\">ed fraction has a 1 in the <\/span><span id=\"P523_527\" class=\"s1 f1699 fs0 l0\">numerator,<br \/>\nTh<\/span><span id=\"P523_529\" class=\"s1 f1699 fs0 l0\">e reciprocal will have a 1 in the <\/span><span id=\"P523_530\" class=\"s1 f1699 fs0 l0\">denominator.<br \/>\n<\/span>Example : If we have numerator as 1 in the simplified fraction like<br \/>\n\\(\\frac{1}{7}\\) then the reciprocal becomes \\(\\frac{7}{1}\\)<br \/>\nso t<span id=\"P523_527\" class=\"s1 f1699 fs0 l0\">h<\/span><span id=\"P523_529\" class=\"s1 f1699 fs0 l0\">e reciprocal will have a 1 in the <\/span><span id=\"P523_530\" class=\"s1 f1699 fs0 l0\">denominator and becomes 7,<br \/>\nSo we get a whole number.<\/span><\/p>\n<p>Question 64.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nYou use \\(\\frac{1}{8}\\) of your battery for every<br \/>\n\\(\\frac{2}{5}\\) of an hour that you video chat.<br \/>\nYou use \\(\\frac{3}{4}\\) of your battery video chatting.<br \/>\nHow long did you video chat?<\/p>\n<p>I had video chat for 2\\(\\frac{2}{5}\\) hours<\/p>\n<p>Explanation:<br \/>\nIf I use \\(\\frac{1}{8}\\) of my battery for every<br \/>\n\\(\\frac{2}{5}\\) of an hour of video chat, then I<br \/>\nuse \\(\\frac{1}{8}\\) \u00f7 \\(\\frac{2}{5}\\) =<br \/>\n\\(\\frac{1}{8}\\) X \\(\\frac{5}{2}\\) =<br \/>\n\\(\\frac{1 x 5}{2 X 16}\\) = \\(\\frac{5}{16}\\) of<br \/>\nmy battery per hour of video chat. \u00a0If I use \\(\\frac{3}{4}\\) of<br \/>\nmy battery for video chatting, I used for \\(\\frac{3}{4}\\) \u00f7<br \/>\n\\(\\frac{5}{16}\\) now \\(\\frac{3}{4}\\) X<br \/>\n\\(\\frac{16}{5}\\)=\\(\\frac{3 X 16}{4 x 5}\\) =<br \/>\n\\(\\frac{48}{20}\\) on further simplification as<br \/>\nboth goes in 4 we get 4 X 12 =48, 4 X 5 = 20, (12,5)=<br \/>\n\\(\\frac{12}{5}\\) as numerator is greater<br \/>\nwe write as ( 2 X 5 + 2 by 5) = 2\\(\\frac{2}{5}\\) hours.<br \/>\nTherefore I had video chat for 2\\(\\frac{2}{5}\\) hours.<\/p>\n<p>Question 65.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nThe table shows the portions of a family budget that are spent on several expenses.<br \/>\na. How many times more is the expense for housing than for automobiles?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27239\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-166.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 166\" width=\"252\" height=\"250\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-166.png 252w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-166-150x150.png 150w\" sizes=\"(max-width: 252px) 100vw, 252px\" \/><br \/>\nb. How many times more is the expense for food than for recreation?<br \/>\nc. The expense for automobile fuel is \\(\\frac{1}{60}\\) of the total expenses.<br \/>\nWhat portion of the automobile expense is spent on fuel?<\/p>\n<p>a. 6 times more is the expense for housing than for automobiles,<br \/>\nb. 17\\(\\frac{7}{9}\\) times more is the expense for<br \/>\nfood than for recreation,<br \/>\nc. \\(\\frac{1}{4}\\) portion of the automobile<br \/>\nexpense is spent on fuel.<\/p>\n<p>Explanation:<br \/>\na. Given we have Portions of Budget for housing is \\(\\frac{2}{5}\\)<br \/>\nand for automobiles as \\(\\frac{1}{15}\\), So the expense<br \/>\nfor housing than for automobiles is \\(\\frac{2}{5}\\) \u00f7<br \/>\n\\(\\frac{1}{15}\\) we write \\(\\frac{1}{15}\\)<br \/>\nas reciprocal and multiply \\(\\frac{2}{5}\\) X \\(\\frac{15}{1}\\) =<br \/>\n\\(\\frac{2 X 15}{5 X 1}\\) = \\(\\frac{30}{5}\\)<br \/>\nwe can simplify as both goes in 5 , 5 X 6 = 30, 5 X 1 = 5,<br \/>\n(6,1),\\(\\frac{30}{5}\\) = 6, therefore 6 times more is<br \/>\nthe expense for housing than for automobiles.<br \/>\nb. Given we have Portions of Budget for food is \\(\\frac{4}{9}\\)<br \/>\nand for recreation is \\(\\frac{1}{40}\\), So the expense for<br \/>\nfood than for recreation is \\(\\frac{4}{9}\\) \u00f7 \\(\\frac{1}{40}\\)<br \/>\nwe write \\(\\frac{1}{40}\\)\u00a0 as reciprocal and multiply<br \/>\n\\(\\frac{4}{9}\\) X \\(\\frac{40}{1}\\) = \\(\\frac{4 X 40}{9 X 1}\\) = \\(\\frac{160}{9}\\) as numerator is greater than<br \/>\ndenominator we write as (17 X 9 + 7 by 9) =<br \/>\n17\\(\\frac{7}{9}\\), therefore 17\\(\\frac{7}{9}\\)<br \/>\ntimes more is the expense for food than for recreation.<br \/>\nc. Given the expense for automobile fuel is \\(\\frac{1}{60}\\)<br \/>\nof the total expenses.<br \/>\nSo the portion of the automobile expense spent on fuel is<br \/>\n\\(\\frac{1}{60}\\) \u00f7 \\(\\frac{1}{15}\\)<br \/>\nwe write \\(\\frac{1}{15}\\)\u00a0 as reciprocal and<br \/>\nmultiply \\(\\frac{1}{60}\\) X \\(\\frac{15}{1}\\) =<br \/>\n\\(\\frac{1 X 15}{60 X 1}\\) = \\(\\frac{15}{60}\\)<br \/>\nwe can simplify further as both goes in 15, 15 X 1 = 15, 15 X 4 = 60,<br \/>\n(1, 4) = \\(\\frac{1}{4}\\), therefore \\(\\frac{1}{4}\\)<br \/>\nportion of the automobile expense is spent on fuel.<\/p>\n<p>Question 66.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nA bottle of juice is \\(\\frac{2}{3}\\) full. The bottle contains<br \/>\n\\(\\frac{4}{5}\\) of a cup of juice.<br \/>\na. Write a division expression that represents the capacity of the bottle.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27240\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-167.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 167\" width=\"178\" height=\"124\" \/><br \/>\nb. Write a related multiplication expression that represents the<br \/>\ncapacity of the bottle.<br \/>\nc. Explain how you can use the diagram to verify the expression in part(b).<br \/>\nd. Find the capacity of the bottle.<br \/>\na. \\(\\frac{4}{5}\\) \u00f7 \\(\\frac{2}{3}\\) represents the<br \/>\ncapacity of the bottle,<br \/>\nb. \\(\\frac{4}{5}\\) X \\(\\frac{3}{2}\\) is the expression<br \/>\nthat represents the capacity of the bottle.<br \/>\nc. <img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-50288\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-35.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-35\" width=\"359\" height=\"159\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-35.bmp 359w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-35-300x133.jpg 300w\" sizes=\"(max-width: 359px) 100vw, 359px\" \/><\/p>\n<p>d. The capacity of the bottle is \\(\\frac{6}{5}\\) cups of juice.<\/p>\n<p>Explanation:<br \/>\na. Given a bottle of juice is \\(\\frac{2}{3}\\) full and bottle<br \/>\ncontains \\(\\frac{4}{5}\\) of a cup of juice, So the division<br \/>\nexpression that represents the capacity of bottle is<br \/>\n\\(\\frac{4}{5}\\) \u00f7 \\(\\frac{2}{3}\\) .<br \/>\nb. Given a bottle of juice is \\(\\frac{2}{3}\\) full and<br \/>\nbottle contains \\(\\frac{4}{5}\\) of a cup of juice,<br \/>\nSo the multiplication expression that represents the capacity of<br \/>\nbottle is we write \\(\\frac{2}{3}\\) as reciprocal \\(\\frac{3}{2}\\)<br \/>\nand multiply \\(\\frac{4}{5}\\) X \\(\\frac{3}{2}\\).<br \/>\nc. We can use the diagram as \\(\\frac{2}{3}\\) = \\(\\frac{4}{5}\\)<br \/>\nand each part in blue represents half of \\(\\frac{4}{5}\\) =<br \/>\n\\(\\frac{1}{2}\\) X \\(\\frac{4}{5}\\) =<br \/>\n\\(\\frac{1 X 4}{2 X 5}\\) = \\(\\frac{4}{10}\\) =<br \/>\n\\(\\frac{2}{5}\\) each part so total parts are 3 X \\(\\frac{2}{5}\\) =<br \/>\n\\(\\frac{6}{5}\\), as shown in the figure, Now we solve with part (b)<br \/>\nas the multiplication expression that represents the capacity of bottle is<br \/>\n\\(\\frac{4}{5}\\) X \\(\\frac{3}{2}\\),we solve<br \/>\n\\(\\frac{4 X 3}{5 X 2}\\) = \\(\\frac{12}{10}\\)<br \/>\nwe further simplify as both goes in 2, 2 X 6 = 12, 2 X 5 = 10,(6,5),<br \/>\n\\(\\frac{6}{5}\\). So by using the diagram we got same results<br \/>\nas \\(\\frac{6}{5}\\) cups of juice is the total capacity of the<br \/>\nbottle so our expression in part(b) is verified.<br \/>\nd. The capacity of the bottle is \\(\\frac{4}{5}\\) X<br \/>\n\\(\\frac{3}{2}\\),we solve \\(\\frac{4 X 3}{5 X 2}\\) =<br \/>\n\\(\\frac{12}{10}\\) we further simplify as both goes in 2,<br \/>\n2 X 6 = 12, 2 X 5 = 10,(6,5),\\(\\frac{6}{5}\\) cups of juice.<\/p>\n<p>Question 67.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nYou have 6 pints of glaze. It takes \\(\\frac{7}{8}\\) of a pint to<br \/>\nglaze a bowl and \\(\\frac{9}{16}\\) of a pint to glaze a plate.<br \/>\na. How many bowls can you completely glaze? How many plates<br \/>\ncan you completely glaze?<br \/>\nb. You want to glaze 5 bowls, and then use the rest for plates.<br \/>\nHow many plates can you completely glaze? How much glaze will be left over?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27241\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-168.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 168\" width=\"269\" height=\"203\" \/><br \/>\nc. How many of each object can you completely glaze so<br \/>\nthat there is no glaze left over? Explain how you found your answer.<br \/>\na. 6 bowls I can completely glaze, 10 plates I can completely glaze,<br \/>\nb. 2 plates , \\(\\frac{1}{2}\\) is left over,<br \/>\nc. 3 bowls and 6 plates,<\/p>\n<p>Explanation:<br \/>\nGiven 6 pints of glaze, It takes \\(\\frac{7}{8}\\) of a pint to glaze<br \/>\na bowl so number of bowls I can completely glaze are<br \/>\n6 \u00f7 \\(\\frac{7}{8}\\) , we write reciprocal of \\(\\frac{7}{8}\\)<br \/>\nand multiply as 6 X \\(\\frac{8}{7}\\) = \\(\\frac{6 X 8}{1 X 7}\\) =<br \/>\n\\(\\frac{48}{7}\\), as numerator is greater we write as<br \/>\n(6 X 7 + 6 by 7) So\u00a0 \\(\\frac{48}{7}\\) =<br \/>\n6\\(\\frac{6}{7}\\)\u2248 6, so 6 bowls I can completely glaze.<br \/>\nIt takes \\(\\frac{9}{16}\\) of a pint to glaze a plate so<br \/>\nnumber of bowls I can completely glaze are 6 \u00f7 \\(\\frac{9}{16}\\) ,<br \/>\nwe write reciprocal of \\(\\frac{9}{16}\\) and multiply as<br \/>\n6 X \\(\\frac{16}{9}\\) = \\(\\frac{6 X 16}{1 X 9}\\) =<br \/>\n\\(\\frac{96}{9}\\) as numerator is greater we write as<br \/>\n( 10 X 9 + 6 by 9) = 10\\(\\frac{6}{9}\\) \u2248 10, so 10 plates<br \/>\nI can completely glaze.<br \/>\nb. So to glaze 5 bowls from 6 pints of glaze it will take,<br \/>\nas we know for 1 bowl it is \\(\\frac{7}{8}\\) of a pint to glaze,<br \/>\nfor 5 bowls it is 5 X \\(\\frac{7}{8}\\) = \\(\\frac{5 X 7}{8}\\) =<br \/>\n\\(\\frac{35}{8}\\) pints to glaze so we use from 6 pints of glaze,<\/p>\n<p>Question 68.<br \/>\n<strong>REASONING<\/strong><br \/>\nA water tank is \\(\\frac{1}{8}\\) full. The tank is<br \/>\n\\(\\frac{3}{4}\\) full when 42 gallons of water are added to the tank.<br \/>\na. How much water can the tank hold?<br \/>\nb. How much water was originally in the tank?<br \/>\nc. How much water is in the tank when it is \\(\\frac{1}{2}\\) full?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27242\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-169.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 169\" width=\"256\" height=\"224\" \/><br \/>\na. The tank can hold 67.2 gallons of water,<br \/>\nb. 8.4 gallons of water was originally in the tank,<br \/>\nc. 33.6 gallons of water is in the tank when it is \\(\\frac{1}{2}\\) full.<\/p>\n<p>Explanation:<br \/>\nGiven a water tank is \\(\\frac{1}{8}\\) full. The tank is<br \/>\n\\(\\frac{3}{4}\\) full when 42 gallons of water are<br \/>\nadded to the tank. Since the tank started at \\(\\frac{1}{8}\\)<br \/>\nfull and reached \\(\\frac{3}{4}\\) full , To find 1 tank full we<br \/>\nhave the difference is \\(\\frac{3}{4}\\) &#8211; \\(\\frac{1}{8}\\) =<br \/>\n42 gallons, So first we make denominators common we<br \/>\nmultiply and divide by 2 to \\(\\frac{3}{4}\\) =<br \/>\n\\(\\frac{6}{8}\\) now we subtract as<br \/>\n\\(\\frac{6}{8}\\) &#8211; \\(\\frac{1}{8}\\) = 42;<br \/>\nas denominators are same we minus numerators (6-1)= 5<br \/>\nmaking \\(\\frac{5}{8}\\) = 42,therefore 1 tank full is<br \/>\n42 X \\(\\frac{8}{5}\\) = \\(\\frac{336}{8}\\) = 67.2 gallons of water.<br \/>\nb. Initially we had \\(\\frac{1}{8}\\) full of water<br \/>\nmeans we had 67.2 X \\(\\frac{1}{8}\\) = 8.4 gallons<br \/>\nof water was originally in the tank,<br \/>\nc. Water in the tank when it is \\(\\frac{1}{2}\\) full is<br \/>\n67.2 X \\(\\frac{1}{2}\\) = \\(\\frac{67.2}{2}\\) =<br \/>\n33.6 gallons of water is in the tank when it is \\(\\frac{1}{2}\\) full.<\/p>\n<h3><a id=\"Lesson_2.3_Dividing_Mixed_Numbers\"><\/a>Lesson 2.3 Dividing Mixed Numbers<\/h3>\n<p><strong>EXPLORATION 1<\/strong><br \/>\n<strong>Dividing Mixed Numbers<\/strong><br \/>\n<strong>Work with a partner. Write a real-life problem that represents each division expression described. Then solve each problem using a model. Check your answers.<\/strong><br \/>\na. How many three-fourths are in four and one-half?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27244\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-170.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 170\" width=\"546\" height=\"88\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-170.png 546w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-170-300x48.png 300w\" sizes=\"(max-width: 546px) 100vw, 546px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27243\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-170.1.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 170.1\" width=\"155\" height=\"158\" \/><br \/>\nb. How many three-eighths are in two and one-fourth?<br \/>\nc. How many one and one-halves are in six?<br \/>\nd. How many seven-sixths are in three and one-third?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27245\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-171.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 171\" width=\"448\" height=\"94\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-171.png 448w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-171-300x63.png 300w\" sizes=\"(max-width: 448px) 100vw, 448px\" \/><br \/>\ne. How many one and one-\ufb01fths are in \ufb01ve?<br \/>\nf. How many three and one-halves are in two and one-half?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27246\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-172.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 172\" width=\"293\" height=\"163\" \/><br \/>\ng. How many four and one-halves are in one and one-half?<\/p>\n<p>a. You have four and one-half of rice, you feed three-fourth to each person,<br \/>\nSo how many persons you can feed .<br \/>\nThere are six, three-fourths in four and one-half.<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-50390\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-36-1.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-36\" width=\"546\" height=\"252\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-36-1.bmp 546w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-36-1-300x138.jpg 300w\" sizes=\"(max-width: 546px) 100vw, 546px\" \/><br \/>\nb. You have two and one-forth bottles of orange juice in that you<br \/>\nadded three -eights cups of water, So how much water is there in<br \/>\ntwo and one-fourth.<br \/>\nThere are six, three-eighths are in two and one-fourth<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-50429\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-37.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-37\" width=\"546\" height=\"198\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-37.bmp 546w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-37-300x109.jpg 300w\" sizes=\"(max-width: 546px) 100vw, 546px\" \/><br \/>\nc. You have 6 meter rope in that how many pieces of one-halves meters<br \/>\nlength ropes you can make.<br \/>\nThere are four, one and one-halves are in six<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-50477\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-38.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-38\" width=\"546\" height=\"165\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-38.bmp 546w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-38-300x91.jpg 300w\" sizes=\"(max-width: 546px) 100vw, 546px\" \/><\/p>\n<p>d. You have three and one-third packets of balloons in that<br \/>\nseven sixth are green color balloons, So how many green balloons are there.<br \/>\nThere are \\(\\frac{20}{7}\\) or 2\\(\\frac{6}{7}\\),<br \/>\nseven-sixths are in three and one-third<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-50546\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-39-1.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-39\" width=\"593\" height=\"165\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-39-1.bmp 593w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-39-1-300x83.jpg 300w\" sizes=\"(max-width: 593px) 100vw, 593px\" \/><br \/>\ne. I have 5 books in which I have completed reading of<br \/>\none and one fifths of books, So how much portions of book<br \/>\nreadings I have completed.<br \/>\nThere are 4\\(\\frac{1}{6}\\) &#8211; one and one-\ufb01fths are in \ufb01ve<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-50602\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-40-2.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-40\" width=\"815\" height=\"201\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-40-2.bmp 815w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-40-2-300x74.jpg 300w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-40-2-768x189.jpg 768w\" sizes=\"(max-width: 815px) 100vw, 815px\" \/><br \/>\nf. I have two and one half of bowls of sweet, I used three and<br \/>\none halves cups of milk to prepare sweet, How many cups of<br \/>\nthree and one halves are there in two and one half of bowls of sweet,<br \/>\nThere are <span style=\"font-size: 16px;\">\\(\\frac{5}{7}\\)&#8211; three and one-halves<br \/>\nare in two and one-half<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-50609\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-41.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-41\" width=\"501\" height=\"201\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-41.bmp 501w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-41-300x120.jpg 300w\" sizes=\"(max-width: 501px) 100vw, 501px\" \/><br \/>\ng. I have one and one-half bag of apples with me,<br \/>\nI gave four and one-halves portion to my friends,<br \/>\nHow many four and one halves portions are there in one and half bag.<br \/>\nThere are \\(\\frac{1}{3}\\) &#8211; four and one-halves are in one and one-half<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-50673\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-42-2.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-42\" width=\"501\" height=\"223\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-42-2.bmp 501w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-42-2-300x134.jpg 300w\" sizes=\"(max-width: 501px) 100vw, 501px\" \/><br \/>\n<\/span><\/p>\n<p>Explanation:<br \/>\na. Three-fourths in four and one-half are 4\\(\\frac{1}{2}\\) \u00f7<br \/>\n\\(\\frac{3}{4}\\) = 4\\(\\frac{1}{2}\\) = (4\u00a0 X 2 + 1 by 2)<br \/>\n= \\(\\frac{9}{2}\\) \u00f7 \\(\\frac{3}{4}\\) =<br \/>\nnow we write \\(\\frac{3}{4}\\) as reciprocal and<br \/>\nmultiply \\(\\frac{9}{2}\\) X \\(\\frac{4}{3}\\) =<br \/>\n\\(\\frac{9 X 4}{2 X 3}\\) = \\(\\frac{36}{6}\\)<br \/>\nas both goes in 6 we get 6 X 6 = 36 and 6 X 1= 6,(6,1),<br \/>\nso \\(\\frac{36}{6}\\) = 6, there are six,<br \/>\nthree-fourths in four and one-half.<\/p>\n<p>b. Three-eighths in two and one-fourth are 2\\(\\frac{1}{4}\\)<br \/>\n\u00f7 \\(\\frac{3}{8}\\) = 2\\(\\frac{1}{4}\\) =<br \/>\n(2\u00a0 X 4 + 1 by 4) = \\(\\frac{9}{4}\\) \u00f7 \\(\\frac{3}{8}\\) =<br \/>\nnow we write \\(\\frac{3}{8}\\) as reciprocal and multiply<br \/>\n\\(\\frac{9}{4}\\) X \\(\\frac{8}{3}\\) =<br \/>\n\\(\\frac{9 X 8}{4 X 3}\\) = \\(\\frac{72}{12}\\)<br \/>\nas both goes in 12 we get 12 X 6 = 72 and 12 X 1= 12,(6,1),<br \/>\nso \\(\\frac{72}{12}\\) = 6,there are six,<br \/>\nthree-eighths are in two and one-fourth.<\/p>\n<p>c. One and one-halves are in six are 6 \u00f7 1\\(\\frac{1}{2}\\),<br \/>\nfirst we write \\(\\frac{1}{2}\\) as (1 x 2 + 1 by 2) =<br \/>\n\\(\\frac{3}{2}\\) now we write reciprocal as \\(\\frac{2}{3}\\)<br \/>\nand multiply with 6 as 6 X \\(\\frac{2}{3}\\) =<br \/>\n\\(\\frac{6 X 2}{1 X 3}\\) =\\(\\frac{12}{3}\\) = 4,<br \/>\nthere are 4, one and one-halves are in six.<\/p>\n<p>d. Seven-sixths are in three and one-third are 3\\(\\frac{1}{3}\\) \u00f7<br \/>\n\\(\\frac{7}{6}\\) , First we write mixed fraction in<br \/>\nfraction as (3 X 3 + 1 by 3) =\u00a0 \\(\\frac{10}{3}\\) now we<br \/>\nwrite reciprocal and multiply as \\(\\frac{10}{3}\\) X<br \/>\n\\(\\frac{6}{7}\\) =\\(\\frac{10 X 6}{3 X 7}\\) =<br \/>\n\\(\\frac{60}{21}\\)\u00a0 as both goes in 3,3 X 20 = 60, 3 X 7 = 21,<br \/>\n(20,7) = \\(\\frac{20}{7}\\) as numerator is greater<br \/>\nwe can write as (2 X 7 + 6 by 7)=2 \\(\\frac{6}{7}\\)<br \/>\nthere are 2 \\(\\frac{6}{7}\\)&#8211; seven-sixths are<br \/>\nin three and one-third .<\/p>\n<p>e. One and one-\ufb01fths in \ufb01ve are 5 \u00f71\\(\\frac{1}{5}\\)<br \/>\nfirst we write mixed fraction as (1 X 5 +1 by 5) =<br \/>\n\\(\\frac{6}{5}\\) now we write reciprocal and<br \/>\nmultiply 5 X \\(\\frac{5}{6}\\) =<br \/>\n\\(\\frac{5 X 5}{6}\\) =\\(\\frac{25}{6}\\)<br \/>\nas numerator is greater we can write as (4 X 6 + 1 by 6) =<br \/>\n4\\(\\frac{1}{6}\\) there are 4\\(\\frac{1}{6}\\) &#8211;<br \/>\none and one-\ufb01fths in \ufb01ve.<\/p>\n<p>f. Three and one-halves are in two and one-half are<br \/>\n2\\(\\frac{1}{2}\\)\u00f7 3\\(\\frac{1}{2}\\)<br \/>\nfirst we write 2\\(\\frac{1}{2}\\) as (2 X 2 + 1 by 2) =<br \/>\n\\(\\frac{5}{2}\\) and 3\\(\\frac{1}{2}\\)<br \/>\nas (3 X 2 + 1 by 2) = \\(\\frac{7}{2}\\).<br \/>\nNow \\(\\frac{5}{2}\\) \u00f7\\(\\frac{7}{2}\\),<br \/>\nWe write reciprocal and multiply as \\(\\frac{5}{2}\\)\u00a0 X<br \/>\n\\(\\frac{2}{7}\\) = \\(\\frac{5 X 2}{2 X 7}\\) =<br \/>\n\\(\\frac{5}{7}\\) there are \\(\\frac{5}{7}\\)<br \/>\n&#8211; three and one-halves are in two and one-half.<\/p>\n<p>g. Four and one-halves are in one and one-half are<br \/>\n1\\(\\frac{1}{2}\\)\u00f7 4\\(\\frac{1}{2}\\)<br \/>\nfirst we write 1\\(\\frac{1}{2}\\) as (1 X 2 + 1 by 2) =<br \/>\n\\(\\frac{3}{2}\\) and 4\\(\\frac{1}{2}\\)<br \/>\nas (4 X 2 + 1 by 2) = \\(\\frac{9}{2}\\).<br \/>\nNow \\(\\frac{3}{2}\\) \u00f7\\(\\frac{9}{2}\\),<br \/>\nWe write reciprocal and multiply as \\(\\frac{3}{2}\\)\u00a0 X<br \/>\n\\(\\frac{2}{9}\\) = \\(\\frac{3 X 2}{2 X 9}\\) =<br \/>\n\\(\\frac{6}{18}\\) as both goes in 6 we get 6 x 1= 6,<br \/>\n6 X 3= 18, (1,3) = \\(\\frac{1}{3}\\) there are<br \/>\n\\(\\frac{1}{3}\\) &#8211; four and one-halves are in one and one-half.<\/p>\n<p><strong>2.3 Lesson<\/strong><\/p>\n<p><strong>Key Idea<\/strong><br \/>\n<strong>Dividing Mixed Numbers<\/strong><br \/>\nWrite each mixed number as an improper fraction.<br \/>\nThen divide as you would with proper fractions.<\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Divide. Write the answer in simplest form.<\/strong><\/p>\n<p>Question 1.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27151\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-173.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 173\" width=\"68\" height=\"46\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27151\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-173.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 173\" width=\"68\" height=\"46\" \/>= 11<br \/>\nExplanation:<br \/>\nGiven expression as 3\\(\\frac{2}{3}\\) \u00f7 \\(\\frac{1}{3}\\),<br \/>\nfirst we write mixed fraction as (3 X 3 + 2 by 3) = \\(\\frac{11}{3}\\) \u00f7<br \/>\n\\(\\frac{1}{3}\\), we write\u00a0 \\(\\frac{1}{3}\\) reciprocal<br \/>\nas \\(\\frac{3}{1}\\) and multiply as \\(\\frac{11}{3}\\) X<br \/>\n\\(\\frac{3}{1}\\) = \\(\\frac{11 X 3}{3 X 1}\\) =<br \/>\n\\(\\frac{11}{1}\\) = 11.<\/p>\n<p>Question 2.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27152\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-174.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 174\" width=\"70\" height=\"57\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27152\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-174.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 174\" width=\"70\" height=\"57\" \/>= \\(\\frac{15}{7}\\) or 2\\(\\frac{1}{7}\\)<br \/>\nExplanation:<br \/>\nGiven expression as 1\\(\\frac{3}{7}\\) \u00f7 \\(\\frac{2}{3}\\),<br \/>\nfirst we write mixed fraction as (1 X 7 + 3 by 7) = \\(\\frac{10}{7}\\) \u00f7<br \/>\n\\(\\frac{2}{3}\\), we write\u00a0 \\(\\frac{2}{3}\\) reciprocal<br \/>\nas \\(\\frac{3}{2}\\) and multiply as \\(\\frac{10}{7}\\) X<br \/>\n\\(\\frac{3}{2}\\) = \\(\\frac{10 X 3}{7 X 2}\\) =<br \/>\n\\(\\frac{30}{14}\\), as both goes in 2, 2 X 15 = 30, 2 X 7 = 14,<br \/>\n(15,7) = \\(\\frac{15}{7}\\) as numerator is greater<br \/>\nwe write as (2 X 7 + 1 by 7), so \\(\\frac{15}{7}\\)= 2\\(\\frac{1}{7}\\).<\/p>\n<p>Question 3.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27247\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-175.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 175\" width=\"64\" height=\"50\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27247\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-175.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 175\" width=\"64\" height=\"50\" \/>= \\(\\frac{26}{9}\\) or 2\\(\\frac{8}{9}\\)<br \/>\nExplanation:<br \/>\nGiven expression as 2\\(\\frac{1}{6}\\) \u00f7 \\(\\frac{3}{4}\\),<br \/>\nfirst we write mixed fraction as (2 X 6 + 1 by 6) = \\(\\frac{13}{6}\\) \u00f7<br \/>\n\\(\\frac{3}{4}\\), we write\u00a0 \\(\\frac{3}{4}\\) reciprocal<br \/>\nas \\(\\frac{4}{3}\\) and multiply as \\(\\frac{13}{6}\\) X<br \/>\n\\(\\frac{4}{3}\\) = \\(\\frac{13 X 4}{6 X 3}\\) =<br \/>\n\\(\\frac{52}{18}\\), as both goes in 2, 2 X 26 = 52,<br \/>\n2 X 9 = 18, (26,9) = \\(\\frac{26}{9}\\) as numerator is<br \/>\ngreater we write as (2 X 9 + 8 by 9),<br \/>\nso \\(\\frac{26}{9}\\)= 2\\(\\frac{8}{9}\\).<\/p>\n<p>Question 4.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27153\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-176.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 176\" width=\"65\" height=\"49\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27153\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-176.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 176\" width=\"65\" height=\"49\" \/>= \\(\\frac{13}{4}\\) or 3\\(\\frac{1}{4}\\)<br \/>\nExplanation:<br \/>\nGiven expression as 6\\(\\frac{1}{2}\\) \u00f7 2, first<br \/>\nwe write mixed fraction as (6 X 2 + 1 by 2) = \\(\\frac{13}{2}\\) \u00f7 2,<br \/>\nwe write 2 reciprocal as \\(\\frac{1}{2}\\) and multiply as<br \/>\n\\(\\frac{13}{2}\\) X \\(\\frac{1}{2}\\) =<br \/>\n\\(\\frac{13 X 1}{2 X 2}\\) = \\(\\frac{13}{4}\\),<br \/>\nas numerator is greater we write as (3 X 4 + 1 by 4),<br \/>\nso \\(\\frac{13}{4}\\)= 3\\(\\frac{1}{4}\\).<\/p>\n<p>Question 5.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27248\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-177.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 177\" width=\"76\" height=\"50\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27248\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-177.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 177\" width=\"76\" height=\"50\" \/>= 4<br \/>\nExplanation:<br \/>\nGiven expressions as 10\\(\\frac{2}{3}\\) \u00f7 2\\(\\frac{2}{3}\\),<br \/>\nFirst we write mixed fractions into fractions as 10\\(\\frac{2}{3}\\)<br \/>\n= (10 X 3 + 2 by 3) = \\(\\frac{32}{3}\\)\u00a0 and 2\\(\\frac{2}{3}\\)<br \/>\n= (2 X 3 + 2 by 3) = \\(\\frac{8}{3}\\),<br \/>\nNow we write as we write \\(\\frac{32}{3}\\) \u00f7<br \/>\n\\(\\frac{8}{3}\\)now reciprocal of the fraction \\(\\frac{8}{3}\\)<br \/>\nas \\(\\frac{3}{8}\\) and multiply as \\(\\frac{32}{3}\\) X<br \/>\n\\(\\frac{3}{8}\\) = \\(\\frac{32 X 3}{3 X 8}\\) =<br \/>\n\\(\\frac{96}{24}\\), we can further simplify as both goes in 24,<br \/>\n24 X 4 = 96 and 24 X 1 = 24, (4,1)= 4.Therefore 10\\(\\frac{2}{3}\\) \u00f7<br \/>\n2\\(\\frac{2}{3}\\) = 4.<\/p>\n<p>Question 6.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27249\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-178.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 178\" width=\"69\" height=\"56\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27249\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-178.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 178\" width=\"69\" height=\"56\" \/>= \\(\\frac{11}{2}\\) or 5\\(\\frac{1}{2}\\)<br \/>\nExplanation:<br \/>\nGiven expressions as 8\\(\\frac{1}{4}\\) \u00f7 1\\(\\frac{1}{2}\\),<br \/>\nFirst we write mixed fractions into fractions as 8\\(\\frac{1}{4}\\) =<br \/>\n(8 X 4 + 1 by 4) = \\(\\frac{33}{4}\\)\u00a0 and 1\\(\\frac{1}{2}\\) =<br \/>\n(1 X 2 + 1 by 2) = \\(\\frac{3}{2}\\), Now we write<br \/>\n\\(\\frac{33}{4}\\) \u00f7 \\(\\frac{3}{2}\\) now reciprocal of<br \/>\nthe fraction \\(\\frac{3}{2}\\) as \\(\\frac{2}{3}\\) and<br \/>\nmultiply as \\(\\frac{33}{4}\\) X \\(\\frac{2}{3}\\) =<br \/>\n\\(\\frac{33 X 2}{4 X 3}\\) = \\(\\frac{66}{12}\\),<br \/>\nwe can further simplify as both goes in 6, 6 X 11 = 66 and 6 X 2 = 12,<br \/>\n(11,2)=\\(\\frac{11}{2}\\) as numerator is greater<br \/>\nwe write as (5 X 2 + 1 by 2) = 5\\(\\frac{1}{2}\\).<br \/>\nTherefore 8\\(\\frac{1}{4}\\) \u00f7 1\\(\\frac{1}{2}\\) =<br \/>\n\\(\\frac{11}{2}\\) or 5\\(\\frac{1}{2}\\).<\/p>\n<p>Question 7.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27250\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-179.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 179\" width=\"67\" height=\"50\" \/><br \/>\n<img decoding=\"async\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-179.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 179\" \/>= \\(\\frac{12}{7}\\) or 1\\(\\frac{5}{7}\\)<br \/>\nExplanation:<br \/>\nGiven expressions as 3 \u00f7 1\\(\\frac{1}{2}\\),First we write<br \/>\nmixed fractions into fractions as 1\\(\\frac{3}{4}\\) =<br \/>\n(1 x 4 + 3 by 4) = \\(\\frac{7}{4}\\) now 3 \u00f7 \\(\\frac{7}{4}\\)<br \/>\nnow reciprocal of the fraction \\(\\frac{7}{4}\\) as<br \/>\n\\(\\frac{4}{7}\\) and multiply as 3 X \\(\\frac{4}{7}\\) =<br \/>\n\\(\\frac{3 X 4}{7}\\) = \\(\\frac{12}{7}\\)<br \/>\nas numerator is greater we write as (1 X 7 + 5 by 7) = 1\\(\\frac{5}{7}\\).<br \/>\nTherefore 3 \u00f7 1\\(\\frac{3}{4}\\) = \\(\\frac{12}{7}\\) or 1\\(\\frac{5}{7}\\).<\/p>\n<p>Question 8.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27251\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-180.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 180\" width=\"62\" height=\"50\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27251\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-180.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 180\" width=\"62\" height=\"50\" \/>= \\(\\frac{3}{10}\\)<br \/>\nExplanation:<br \/>\nGiven expressions as \\(\\frac{3}{4}\\) \u00f7 2\\(\\frac{1}{2}\\),<br \/>\nFirst we write mixed fractions into fractions as 2\\(\\frac{1}{2}\\) =<br \/>\n(2 x 2 + 1 by 2) = \\(\\frac{5}{2}\\) now \\(\\frac{3}{4}\\) \u00f7<br \/>\n\\(\\frac{5}{2}\\) now reciprocal of the fraction<br \/>\n\\(\\frac{5}{2}\\) as \\(\\frac{2}{5}\\) and multiply as<br \/>\n\\(\\frac{3}{4}\\) X \\(\\frac{2}{5}\\) =<br \/>\n\\(\\frac{3 X 2}{4 X 5}\\) = \\(\\frac{6}{20}\\)<br \/>\nas both goes in 2, 2 X 3 = 6, 2 X 10= 20, (3,10)= \\(\\frac{3}{10}\\).<br \/>\nTherefore \\(\\frac{3}{4}\\) \u00f7 2\\(\\frac{1}{2}\\) = \\(\\frac{3}{10}\\).<\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Evaluate the expression. Write the answer in simplest form.<\/strong><\/p>\n<p>Question 9.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27154\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-181.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 181\" width=\"89\" height=\"54\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27154\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-181.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 181\" width=\"89\" height=\"54\" \/>= \\(\\frac{65}{8}\\) = 8\\(\\frac{1}{8}\\)<br \/>\nExplanation:<br \/>\nGiven expressions as (1\\(\\frac{1}{2}\\) \u00f7 \\(\\frac{1}{6}\\)) &#8211;<br \/>\n\\(\\frac{7}{8}\\) ,First we write mixed fractions into fractions as<br \/>\n1\\(\\frac{1}{2}\\) = (1 x 2 + 1 by 2) = \\(\\frac{3}{2}\\)<br \/>\nnow \\(\\frac{3}{2}\\) \u00f7 \\(\\frac{1}{6}\\) now reciprocal<br \/>\nof the fraction \\(\\frac{1}{6}\\) as 6 and multiply as<br \/>\n\\(\\frac{3}{2}\\) X 6 = \\(\\frac{3 X 6}{2 X 1}\\) =<br \/>\n\\(\\frac{18}{2}\\) as both goes in 2, 2 X 9 = 18, 2 X 1= 2, (9,1)=9.<br \/>\nNow 9 &#8211; \\(\\frac{7}{8}\\) =(9 X 8 &#8211; 7 by 8) = \\(\\frac{65}{8}\\)<br \/>\nas numerator is greater we write as (8 X 8 + 1 by 8) = \\(\\frac{65}{8}\\) =<br \/>\n8\\(\\frac{1}{8}\\). Therefore (1\\(\\frac{1}{2}\\) \u00f7 \\(\\frac{1}{6}\\)) &#8211;<br \/>\n\\(\\frac{7}{8}\\) = \\(\\frac{65}{8}\\) = 8\\(\\frac{1}{8}\\).<\/p>\n<p>Question 10.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27252\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-182.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 182\" width=\"92\" height=\"47\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27252\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-182.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 182\" width=\"92\" height=\"47\" \/>= \\(\\frac{44}{9}\\) = 4\\(\\frac{8}{9}\\)<br \/>\nExplanation:<br \/>\nGiven expressions as (3\\(\\frac{1}{3}\\) \u00f7 \\(\\frac{5}{6}\\)) +<br \/>\n\\(\\frac{8}{9}\\) ,First we write mixed fractions into fractions as<br \/>\n3\\(\\frac{1}{3}\\) = (3 x 3 + 1 by 3) = \\(\\frac{10}{3}\\)<br \/>\nnow \\(\\frac{10}{3}\\) \u00f7 \\(\\frac{5}{6}\\) now reciprocal<br \/>\nof the fraction \\(\\frac{5}{6}\\) as \\(\\frac{6}{5}\\) and multiply as<br \/>\n\\(\\frac{10}{3}\\) X \\(\\frac{6}{5}\\) = \\(\\frac{10 X 6}{3 X 5}\\) =<br \/>\n\\(\\frac{60}{15}\\) as both goes in 15, 15 X 4 = 60, 15 X 1= 15, (4,1)=4.<br \/>\nNow 4 + \\(\\frac{8}{9}\\) =(4 X 9 + 8 by 9) = \\(\\frac{44}{9}\\)<br \/>\nas numerator is greater we write as (4 X 9 + 8 by 9) = \\(\\frac{44}{9}\\) =<br \/>\n4\\(\\frac{8}{9}\\). Therefore (3\\(\\frac{1}{3}\\) \u00f7 \\(\\frac{5}{6}\\)) +<br \/>\n\\(\\frac{8}{9}\\) = \\(\\frac{44}{9}\\) = 4\\(\\frac{8}{9}\\).<\/p>\n<p>Question 11.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27155\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-183.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 183\" width=\"103\" height=\"52\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27155\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-183.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 183\" width=\"103\" height=\"52\" \/>= \\(\\frac{8}{5}\\) = 1\\(\\frac{3}{5}\\)<br \/>\nExplanation:<br \/>\nGiven expressions as \\(\\frac{2}{5}\\) + 2\\(\\frac{4}{5}\\) \u00f7 2,<br \/>\nFirst we write mixed fractions into fractions as<br \/>\n2\\(\\frac{4}{5}\\) = (2 x 5 + 4 by 5) = \\(\\frac{14}{5}\\)<br \/>\nnow \\(\\frac{2}{5}\\) + \\(\\frac{14}{5}\\) as denominators<br \/>\nare same we add numerators as 2 + 14 and write as \\(\\frac{16}{5}\\),<br \/>\nnow we divide with 2, \\(\\frac{16}{5}\\) \u00f7 2, we write 2 as<br \/>\nreciprocal and multiply \\(\\frac{16}{5}\\) X \\(\\frac{1}{2}\\) =<br \/>\n\\(\\frac{16 X 1}{5 X 2}\\) = \\(\\frac{16}{10}\\) as both goes<br \/>\nin 2, 2 x 8 = 16, 2 X 5 = 10, (8,5) = \\(\\frac{8}{5}\\) as numerator is<br \/>\ngreater we write as (1 X 5 + 3 by 5) = 1\\(\\frac{3}{5}\\) ,Therefore<br \/>\n\\(\\frac{2}{5}\\) + 2\\(\\frac{4}{5}\\) \u00f7 2 =<br \/>\n\\(\\frac{8}{5}\\) = 1\\(\\frac{3}{5}\\) .<\/p>\n<p>Question 12.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27253\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-184.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 184\" width=\"107\" height=\"53\" \/><br \/>\n<img decoding=\"async\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-184.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 184\" \/>= \\(\\frac{1}{3}\\)<br \/>\nExplanation:<br \/>\nGiven expressions as \\(\\frac{2}{3}\\) &#8211; (1\\(\\frac{4}{7}\\) \u00f7 4\\(\\frac{5}{7})\\),First we write mixed fractions into fractions as<br \/>\n1\\(\\frac{4}{7}\\) = (1 X 7 + 4 by 7) = \\(\\frac{11}{7}\\) and<br \/>\n4\\(\\frac{5}{7}\\) = (4 X 7 + 5 by 7) = \\(\\frac{33}{7}\\),<br \/>\nNow first we divide \\(\\frac{11}{7}\\) \u00f7 \\(\\frac{33}{7}\\) =<br \/>\nwe write \\(\\frac{33}{7}\\) as reciprocal and multiply \\(\\frac{7}{33}\\) ,<br \/>\n\\(\\frac{11}{7}\\) X \\(\\frac{7}{33}\\) = \\(\\frac{11 X 7}{7 X 33}\\) =<br \/>\n\\(\\frac{77}{231}\\) as both goes in 77, 77 X 1= 77, 77 X 3 = 231,(1,3),<br \/>\n\\(\\frac{1}{3}\\) now we subtract from \\(\\frac{2}{3}\\) &#8211; \\(\\frac{1}{3}\\)<br \/>\nas denominators are same we subtract from numerators as<br \/>\n(2-1) we get \\(\\frac{1}{3}\\), Therefore \\(\\frac{2}{3}\\) &#8211; (1\\(\\frac{4}{7}\\) \u00f7 4\\(\\frac{5}{7})\\) = \\(\\frac{1}{3}\\).<\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><br \/>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p><strong>EVALUATING EXPRESSIONS<\/strong><br \/>\n<strong>Evaluate the expression. Write the answer in simplest form.<\/strong><\/p>\n<p>Question 13.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27156\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-185.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 185\" width=\"59\" height=\"48\" \/><br \/>\n<img decoding=\"async\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-185.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 185\" \/>= \\(\\frac{224}{28}\\) = 8.<br \/>\nExplanation:<br \/>\nGiven expressions as 4\\(\\frac{4}{7}\\) \u00f7 \\(\\frac{4}{7}\\),<br \/>\nFirst we write mixed fractions into fractions 4\\(\\frac{4}{7}\\) as<br \/>\n(4 X 7 + 4 by 7) = \\(\\frac{32}{7}\\), Now \\(\\frac{4}{7}\\) we<br \/>\nwrite as reciprocal and multiply \\(\\frac{7}{4}\\) as<br \/>\n\\(\\frac{32}{7}\\) X \\(\\frac{7}{4}\\) = \\(\\frac{32 X 7}{7 X 4}\\)=<br \/>\n\\(\\frac{224}{28}\\) as both goes in 28, 28 X 8 = 224,<br \/>\n28 X 1 = 28, (8,1) = 8, therefore 4\\(\\frac{4}{7}\\) \u00f7 \\(\\frac{4}{7}\\)=<br \/>\n\\(\\frac{224}{28}\\) = 8.<\/p>\n<p>Question 14.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27254\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-186.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 186\" width=\"77\" height=\"51\" \/><br \/>\n<img decoding=\"async\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-186.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 186\" \/>= \\(\\frac{2}{21}\\)<br \/>\nExplanation:<br \/>\nGiven expressions as \\(\\frac{1}{2}\\) \u00f7 5\\(\\frac{1}{4}\\),<br \/>\nFirst we write mixed fractions into fractions 5\\(\\frac{1}{4}\\) as<br \/>\n(5 X 4 + 1 by 4) = \\(\\frac{21}{4}\\) we write as reciprocal and<br \/>\nmultiply \\(\\frac{4}{21}\\) as \\(\\frac{1}{2}\\) X \\(\\frac{4}{21}\\) =<br \/>\n\\(\\frac{1 X 4}{2 X 21}\\) = \\(\\frac{4}{42}\\) as both goes in<br \/>\n2, 2 X 2 = 4, 2 X 21 = 42, (2, 21) = \\(\\frac{2}{21}\\), therefore<br \/>\n\\(\\frac{1}{2}\\) \u00f7 5\\(\\frac{1}{4}\\) = \\(\\frac{2}{21}\\).<\/p>\n<p>Question 15.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27255\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-187.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 187\" width=\"99\" height=\"55\" \/><br \/>\n<img decoding=\"async\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-187.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 187\" \/>= \\(\\frac{19}{4}\\) = 4\\(\\frac{3}{4}\\)<br \/>\nExplanation:<br \/>\nGiven expressions as \\(\\frac{3}{4}\\) + (6\\(\\frac{2}{5}\\) \u00f7<br \/>\n1\\(\\frac{3}{5}\\)), First we write mixed fractions into fractions as<br \/>\n6\\(\\frac{2}{5}\\) = (6 X 5 + 2 by 5) = \\(\\frac{32}{5}\\) and<br \/>\n1\\(\\frac{3}{5}\\) = (1 X 5 + 3 by 5) = \\(\\frac{8}{5}\\),<br \/>\nwe write reciprocal \\(\\frac{5}{8}\\) and multiply \\(\\frac{32}{5}\\) X \\(\\frac{5}{8}\\) = \\(\\frac{32 X 5}{5 X 8}\\) = \\(\\frac{160}{40}\\)<br \/>\nas both goes in 40 as 40 X 4 = 160, 40 X 1 = 40, (4,1), \\(\\frac{160}{40}\\) =4,<br \/>\nNow \\(\\frac{3}{4}\\) + 4 = ( 3 + 4 X 4 by 4 ) = \\(\\frac{19}{4}\\),<br \/>\nas numerator is greater we write as ( 4 X 4 + 3 by 4) = 4\\(\\frac{3}{4}\\),<br \/>\ntherefore \\(\\frac{3}{4}\\) + (6\\(\\frac{2}{5}\\) \u00f7<br \/>\n1\\(\\frac{3}{5}\\)) = \\(\\frac{19}{4}\\) = 4\\(\\frac{3}{4}\\).<\/p>\n<p>Question 16.<br \/>\n<strong>NUMBER SENSE<\/strong><br \/>\nIs 2\\(\\frac{1}{2}\\) \u00f7 1\\(\\frac{1}{4}\\) the same as 1\\(\\frac{1}{4}\\) \u00f7 2\\(\\frac{1}{2}\\)? Use models to justify your answer.<br \/>\nNo,Is 2\\(\\frac{1}{2}\\) \u00f7 1\\(\\frac{1}{4}\\) is not the same as<br \/>\n1\\(\\frac{1}{4}\\) \u00f7 2\\(\\frac{1}{2}\\)<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-50702\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-46.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-46\" width=\"488\" height=\"305\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-46.bmp 488w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-46-300x188.jpg 300w\" sizes=\"(max-width: 488px) 100vw, 488px\" \/><\/p>\n<p>Explanation:<br \/>\nGiven expressions as 2\\(\\frac{1}{2}\\) \u00f7 1\\(\\frac{1}{4}\\) and<br \/>\n1\\(\\frac{1}{4}\\) \u00f7 2\\(\\frac{1}{2}\\) first we write mixed fractions,<br \/>\ninto fractions 2\\(\\frac{1}{2}\\) = (2 X 2 + 1 by 2) = \\(\\frac{5}{2}\\),<br \/>\n1\\(\\frac{1}{4}\\) = (1 X 4 + 1 by 4) = \\(\\frac{5}{4}\\), now<br \/>\nwrite as reciprocal as \\(\\frac{4}{5}\\), now we multiply as<br \/>\n\\(\\frac{5}{2}\\) X \\(\\frac{4}{5}\\) = \\(\\frac{5 x 4}{2 X 5}\\) =<br \/>\n\\(\\frac{20}{10}\\) as both goes in 10, 10 X 2 = 20, 10 X 1= 10,(2,1)=2.<br \/>\nNow 1\\(\\frac{1}{4}\\) \u00f7 2\\(\\frac{1}{2}\\) we write mixed fractions,<br \/>\ninto fractions 1\\(\\frac{1}{4}\\) = (1 X 4 + 1 by 4) = \\(\\frac{5}{4}\\),<br \/>\n2\\(\\frac{1}{2}\\) = (2 X 2 + 1 by 2) = \\(\\frac{5}{2}\\), now<br \/>\nwrite as reciprocal as \\(\\frac{2}{5}\\), now we multiply as<br \/>\n\\(\\frac{5}{4}\\) X \\(\\frac{2}{5}\\) = \\(\\frac{5 x 2}{4 X 5}\\) =<br \/>\n\\(\\frac{10}{20}\\) = as both goes in 10, 10 X 1 = 10, 10 X 2 = 20, (1,2) =<br \/>\n\\(\\frac{1}{2}\\), therefore 2 \u2260 \\(\\frac{1}{2}\\) So no,<br \/>\n2\\(\\frac{1}{2}\\) \u00f7 1\\(\\frac{1}{4}\\) is not the same as<br \/>\n1\\(\\frac{1}{4}\\) \u00f7 2\\(\\frac{1}{2}\\).<\/p>\n<p>Question 17.<br \/>\n<strong>DIFFERENT WORDS, SAME QUESTION<\/strong><br \/>\nWhich is different? Find \u201cboth\u201d answers.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27157\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-188.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 188\" width=\"473\" height=\"119\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-188.png 473w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-188-300x75.png 300w\" sizes=\"(max-width: 473px) 100vw, 473px\" \/><br \/>\nd. Different one is What is \\(\\frac{1}{8}\\) of 5 \\(\\frac{1}{2}\\) =<br \/>\n5\\(\\frac{1}{2}\\) multiplied by \\(\\frac{1}{8}\\).<br \/>\nAll 3 results are in whole only \\(\\frac{1}{8}\\) of 5 \\(\\frac{1}{2}\\)<br \/>\nis in fraction. So it is different from other 3 ones.<\/p>\n<p>Explanation:<br \/>\nWe calculate first 5\\(\\frac{1}{2}\\) = (5 X 2 + 1 by 2) = \\(\\frac{11}{2}\\)<br \/>\na. As what is 5\\(\\frac{1}{2}\\) divided by \\(\\frac{1}{8}\\) means<br \/>\n5\\(\\frac{1}{2}\\) \u00f7 \\(\\frac{1}{8}\\),<br \/>\n\\(\\frac{11}{2}\\) \u00f7\u00a0 \\(\\frac{1}{8}\\),<br \/>\nwe write reciprocal and multiply as<br \/>\n\\(\\frac{11}{2}\\) X\u00a0 8 = \\(\\frac{88}{2}\\) = 44.<br \/>\nb. What is quotient of 5\\(\\frac{1}{2}\\) and \\(\\frac{1}{8}\\) means<br \/>\n5\\(\\frac{1}{2}\\) \u00f7 \\(\\frac{1}{8}\\),<br \/>\n\\(\\frac{11}{2}\\) \u00f7\u00a0 \\(\\frac{1}{8}\\),<br \/>\nwe write reciprocal and multiply as<br \/>\n\\(\\frac{11}{2}\\) X\u00a0 8 = \\(\\frac{88}{2}\\) = 44.<br \/>\nc. What is 5\\(\\frac{1}{2}\\) times of 8 means<br \/>\n5\\(\\frac{1}{2}\\) X 8=\u00a0 \\(\\frac{88}{2}\\) = 44.<br \/>\nd. What is \\(\\frac{1}{8}\\) of 5\\(\\frac{1}{2}\\) means<br \/>\n5\\(\\frac{1}{2}\\) X \\(\\frac{1}{8}\\),<br \/>\n\\(\\frac{11}{2}\\) X \\(\\frac{1}{8}\\) = \\(\\frac{11}{16}\\)=0.6875,<br \/>\nSo only different one is d. What is \\(\\frac{1}{8}\\) of 5 \\(\\frac{1}{2}\\)<br \/>\nvalue is different from the other 3.<\/p>\n<p><strong>Self-Assessment for Problem Solving<\/strong><br \/>\n<strong>Solve each exercise. Then rate your understanding of the success criteria in your journal.<\/strong><\/p>\n<p>Question 18.<br \/>\nA water cooler contains 160 cups of water. During practice, each person on a team \ufb01lls a water bottle with 3\\(\\frac{1}{3}\\) cups of water from the cooler. Is there enough water for all 45 people on the team to \ufb01ll their water bottles? Explain.<br \/>\n150 cups\u00a0 of water is required for 45 people and cooler contains<br \/>\n160 cups of water, therefore we have sufficient enough water<br \/>\nfor all 45 people on the team to \ufb01ll their water bottles.<\/p>\n<p>Explanation:<br \/>\nGiven a water cooler contains 160 cups of water, During practice,<br \/>\neach person on a team \ufb01lls a water bottle with 3\\(\\frac{1}{3}\\) cups<br \/>\nof water from the cooler. To find is there enough water for all<br \/>\n45 people on the team to \ufb01ll their water bottles we calculate as<br \/>\n45 persons X 3\\(\\frac{1}{3}\\) =<br \/>\nfirst we write mixed fraction as fraction 3\\(\\frac{1}{3}\\) =<br \/>\n(3 X 3 +1 by 3) = \\(\\frac{10}{3}\\) now we multiply as<br \/>\n45\u00a0 X \\(\\frac{10}{3}\\) = \\(\\frac{450}{3}\\) as both<br \/>\ngoes in 3, 3 X 150 = 450,3 x 1= 3, (150,1) so \\(\\frac{450}{3}\\)= 150 cups<br \/>\nof water is required for 45 people and cooler contains 160 cups of water,<br \/>\ntherefore we have sufficient enough water for all 45 people on the team to<br \/>\n\ufb01ll their water bottles.<\/p>\n<p>Question 19.<br \/>\nA cyclist is 7\\(\\frac{3}{4}\\) kilometers from the \ufb01nish line of a race. The cyclist rides at a rate of 25\\(\\frac{5}{6}\\) kilometers per hour. How many minutes will it take the cyclist to \ufb01nish the race?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27256\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-189.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 189\" width=\"227\" height=\"232\" \/><\/p>\n<p>It will take 18 minutes for the cyclist to \ufb01nish the race,<\/p>\n<p>Explanation:<br \/>\nGiven a cyclist is 7\\(\\frac{3}{4}\\) kilometers from the \ufb01nish line of a race,<br \/>\nThe cyclist rides at a rate of 25\\(\\frac{5}{6}\\) kilometers per hour,<br \/>\nmeans we write as 25\\(\\frac{5}{6}\\) \u00f7\u00a0 7\\(\\frac{3}{4}\\)<br \/>\nfirst we write mixed fractions in fractions as 25\\(\\frac{5}{6}\\) =<br \/>\n(25 X 6 + 5 by 6) = \\(\\frac{155}{6}\\) now 7\\(\\frac{3}{4}\\) =<br \/>\n(7 X 4 + 3 by 4) = \\(\\frac{31}{4}\\) now reciprocal of \\(\\frac{31}{4}\\) =<br \/>\n\\(\\frac{4}{31}\\) and multiply as \\(\\frac{155}{6}\\) X \\(\\frac{4}{31}\\)=<br \/>\n\\(\\frac{155 X 4}{6 X 31}\\) = \\(\\frac{620}{186}\\) kilometers<br \/>\nin an hour. Now we convert into minutes as \\(\\frac{186 X 60}{620}\\) =<br \/>\n\\(\\frac{11160}{620}\\) as both goes in 620, 620 X 18 = 11160, 620 X 1 = 620,<br \/>\n\\(\\frac{11160}{620}\\) = 18 minutes.Therefore it will take<br \/>\n18 minutes for the cyclist to \ufb01nish the race.<\/p>\n<h3><a id=\"Dividing_Mixed_Numbers_Homework_&amp;_Practice_2.3\"><\/a>Dividing Mixed Numbers Homework &amp; Practice 2.3<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p>Divide. Write the answer in simplest form.<\/p>\n<p>Question 1.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27257\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-190.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 190\" width=\"53\" height=\"40\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27257\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-190.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 190\" width=\"53\" height=\"40\" \/>= \\(\\frac{7}{8}\\)<br \/>\nExplanation:<br \/>\nGiven expression as \\(\\frac{1}{8}\\) \u00f7 \\(\\frac{1}{7}\\)<br \/>\nwe write reciprocal of the fraction \\(\\frac{1}{7}\\) as<br \/>\n\\(\\frac{7}{1}\\) and multiply as \\(\\frac{1}{8}\\) X<br \/>\n\\(\\frac{7}{1}\\) = \\(\\frac{1 X 7}{8 X 1}\\) =<br \/>\n\\(\\frac{7}{8}\\), Therefore \\(\\frac{1}{8}\\) \u00f7 \\(\\frac{1}{7}\\) = \\(\\frac{7}{8}\\).<\/p>\n<p>Question 2.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27158\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-191.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 191\" width=\"56\" height=\"49\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27158\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-191.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 191\" width=\"56\" height=\"49\" \/>= \\(\\frac{7}{6}\\) or 1\\(\\frac{1}{6}\\)<br \/>\nExplanation:<br \/>\nGiven expression as \\(\\frac{7}{9}\\) \u00f7 \\(\\frac{2}{3}\\)<br \/>\nwe write reciprocal of the fraction \\(\\frac{2}{3}\\) as<br \/>\n\\(\\frac{3}{2}\\) and multiply as \\(\\frac{7}{9}\\) X<br \/>\n\\(\\frac{3}{2}\\) = \\(\\frac{7 X 3}{9 X 2}\\) =<br \/>\n\\(\\frac{21}{18}\\) as both goes in 3, 3 X 7 =21, 3 X 6 = 18,(7,6)=<br \/>\n\\(\\frac{7}{6}\\) as numerator is greater we write as (1 X 6 + 1 by 6)=<br \/>\n1\\(\\frac{1}{6}\\). Therefore \\(\\frac{7}{9}\\) \u00f7 \\(\\frac{2}{3}\\) = \\(\\frac{7}{6}\\) or 1\\(\\frac{1}{6}\\).<\/p>\n<p>Question 3.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27258\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-192.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 192\" width=\"56\" height=\"49\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27258\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-192.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 192\" width=\"56\" height=\"49\" \/>= \\(\\frac{1}{12}\\)<br \/>\nExplanation:<br \/>\nGiven expression as \\(\\frac{5}{6}\\) \u00f7 10<br \/>\nwe write reciprocal for 10 as \\(\\frac{1}{10}\\)<br \/>\nand multiply as \\(\\frac{5}{6}\\) X \\(\\frac{1}{10}\\) =<br \/>\n\\(\\frac{5 X 1}{6 X 10}\\) = \\(\\frac{5}{60}\\) as both goes in 5,<br \/>\n5 X 1 = 5, 5 X 12 = 60 ,(1,12) = \\(\\frac{1}{12}\\),<br \/>\nTherefore \\(\\frac{5}{6}\\) \u00f7 10 = \\(\\frac{1}{12}\\).<\/p>\n<p>Question 4.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27259\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-193.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 193\" width=\"64\" height=\"53\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27259\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-193.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 193\" width=\"64\" height=\"53\" \/>= 32<br \/>\nExplanation:<br \/>\nGiven expression as 12 \u00f7 \\(\\frac{3}{8}\\), we write reciprocal<br \/>\nfor \\(\\frac{3}{8}\\) as \\(\\frac{8}{3}\\) and multiply as<br \/>\n12 X \\(\\frac{8}{3}\\) = \\(\\frac{12 X 8}{1 X 3}\\) = \\(\\frac{96}{3}\\),<br \/>\nas both goes in 3, 3 X 32 = 96, 3 X 1 = 3, (32,1), So \\(\\frac{96}{3}\\) = 32,<br \/>\nTherefore 12 \u00f7 \\(\\frac{3}{8}\\) = 32.<\/p>\n<p><strong>Find the LCM of the numbers.<\/strong><\/p>\n<p>Question 5.<br \/>\n8, 14<br \/>\nThe LCM of 8, 14 is 56<\/p>\n<p>Explanation:<br \/>\nThe prime factorization of 8 is\u00a0 2 X 2 X 2,<br \/>\n<span style=\"font-size: 16px;\">The prime factorization of 14 is 2 X 7,<br \/>\n<\/span>Eliminate the duplicate factors of the two lists,<br \/>\n(we have 2 in common both ),then multiply them once<br \/>\nwith the remaining factors of the lists to get<br \/>\nLCM(8, 14) = 2 X 2 X 2 X 7 = 56.<\/p>\n<p>Question 6.<br \/>\n9, 11, 12<br \/>\nThe LCM of 9, 11, 12\u00a0 is 396<\/p>\n<p>Explanation:<br \/>\nThe factors of 9 is\u00a0 3 X 3,<br \/>\n<span style=\"font-size: 16px;\">The factors of 11 is 11,<br \/>\nThe factors of 12 is 3 X 4<br \/>\n<\/span>Eliminate the duplicate factors of the two lists,<br \/>\n(we have 3 in common),then multiply them once<br \/>\nwith the remaining factors of the lists to get<br \/>\nLCM(9, 11, 12) = 3 X 3 X 11 X 4 = 396.<\/p>\n<p>Question 7.<br \/>\n12, 27, 30<br \/>\nThe LCM of 12, 27, 30\u00a0 is 540<\/p>\n<p>Explanation:<br \/>\nThe factors of 12 is\u00a0 3 X 4 =\u00a0 3 X 2 X 2<br \/>\n<span style=\"font-size: 16px;\">The factors of 27 is 3 X 9 = 3 X 3 X 3,<br \/>\nThe factors of 30 is 3 X 10 = 3 X 2 X 5<br \/>\n<\/span>Eliminate the duplicate factors of the two lists,<br \/>\n(we have 2, 3 in common),then multiply them once<br \/>\nwith the remaining factors of the lists to get<br \/>\nLCM(12, 27, 30) = 2 X 3 X 9 X 10 = 540.<\/p>\n<p><strong>Find the volume of the rectangular prism.<\/strong><\/p>\n<p>Question 8.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27260\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-194.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 194\" width=\"131\" height=\"165\" \/><br \/>\nThe volume of the rectangular prism is 96 mt<sup>3<\/sup><\/p>\n<p>Explanation:<br \/>\nGiven length as 4 m, width as 3 m and height as 8 m,<br \/>\nwe know the volume of the rectangular prism is<br \/>\nlength X width X height =\u00a0 4 X 3 X 8 = 96, Therefore<br \/>\nthe volume of the rectangular prism is 96 mt<sup>3<\/sup>.<\/p>\n<p>Question 9.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27261\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-195.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 195\" width=\"134\" height=\"152\" \/><br \/>\nThe volume of the rectangular prism is 70 in<sup>3<\/sup><\/p>\n<p>Explanation:<br \/>\nGiven length as 5 in, width as 2 in and height as 7 in,<br \/>\nwe know the volume of the rectangular prism is<br \/>\nlength X width X height =\u00a0 5 X 2 X 7 = 70, Therefore<br \/>\nthe volume of the rectangular prism is 70 in<sup>3<\/sup>.<\/p>\n<p>Question 10.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27262\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-196.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 196\" width=\"184\" height=\"102\" \/><br \/>\nThe volume of the rectangular prism is 240 yd<sup>3<\/sup><\/p>\n<p>Explanation:<br \/>\nGiven length as 10 yd, width as 8 yd and height as 3 yd,<br \/>\nwe know the volume of the rectangular prism is<br \/>\nlength X width X height =\u00a0 10 X 8 X 3 = 240, Therefore<br \/>\nthe volume of the rectangular prism is 240 yd<sup>3<\/sup>.<\/p>\n<p>Question 11.<br \/>\nWhich number is not a prime factor of 286?<br \/>\nA. 2<br \/>\nB. 7<br \/>\nC. 11<br \/>\nD. 13<\/p>\n<p>B. 7 is not a prime factor of 286,<\/p>\n<p>Explanation:<br \/>\n<span style=\"font-size: 16px;\">286 is a composite number.<br \/>\n<\/span>Prime factorization of 286 = 2 x 11 x 13 and<br \/>\nFactors of 286 are 1, 2, 11, 13, 22, 26, 143, 286.<br \/>\nTherefore 7 is not a prime factor of 286.<\/p>\n<p><strong>Concepts, Skills, &amp; Problem Solving<\/strong><br \/>\n<strong>CHOOSE TOOLS<\/strong><br \/>\n<strong>Write a real-life problem that represents the division expression described. Then solve the problem using a model. Check your answer algebraically.<\/strong> (See Exploration 1, p. 61.)<\/p>\n<p>Question 12.<br \/>\nHow many two-thirds are in three and one-third?<br \/>\nI have three and one- third rose flowers I have, I distributed among<br \/>\ntwo-thirds children, how man children are there?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-50796\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-47.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-47\" width=\"533\" height=\"176\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-47.bmp 533w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-47-300x99.jpg 300w\" sizes=\"(max-width: 533px) 100vw, 533px\" \/><\/p>\n<p>Five, two-thirds are in three and one-third<\/p>\n<p>Explanation:<br \/>\nGiven to find two-thirds are in three and one-third means<br \/>\n3\\(\\frac{1}{3}\\) \u00f7 \\(\\frac{2}{3}\\), First we write<br \/>\nmixed fraction as ( 3 X 3 + 1 by 3) = \\(\\frac{10}{3}\\)\u00f7 \\(\\frac{2}{3}\\)<br \/>\nwe write reciprocal of the fraction \\(\\frac{2}{3}\\)<br \/>\nas \\(\\frac{3}{2}\\) and multiply \\(\\frac{10}{3}\\) X<br \/>\n\\(\\frac{3}{2}\\) = \\(\\frac{10 X 3}{3 X 2}\\)= \\(\\frac{30}{6}\\)<br \/>\nas both goes in 6 as 6 X 5 = 30, 6 X 1= 6,(5, 1), \\(\\frac{30}{6}\\) = 5.<\/p>\n<p>Question 13.<br \/>\nHow many one and one-sixths are in \ufb01ve and \ufb01ve-sixths?<br \/>\nA golden statue is \ufb01ve and \ufb01ve-sixths tall and a silver statue is<br \/>\none and one-sixths tall, How many times is the golden statue<br \/>\ntaller than silver statue.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-50801\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-48-1.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-48\" width=\"753\" height=\"195\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-48-1.bmp 753w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-48-1-300x78.jpg 300w\" sizes=\"(max-width: 753px) 100vw, 753px\" \/><\/p>\n<p>Five, one and one-sixths are in \ufb01ve and \ufb01ve-sixths<\/p>\n<p>Explanation:<br \/>\nGiven to find one and one-sixths are in \ufb01ve and \ufb01ve-sixths means<br \/>\n5\\(\\frac{5}{6}\\) \u00f7 1\\(\\frac{1}{6}\\), First we write<br \/>\n5\\(\\frac{5}{6}\\) mixed fraction as ( 5 X 6 + 5 by 6) = \\(\\frac{35}{6}\\)<br \/>\nand 1\\(\\frac{1}{6}\\) mixed fraction as (1 X 6 + 1 by 6)= \\(\\frac{7}{6}\\).<br \/>\nNow \\(\\frac{35}{6}\\) \u00f7 \\(\\frac{7}{6}\\) we write reciprocal<br \/>\nof the fraction \\(\\frac{7}{6}\\) as \\(\\frac{6}{7}\\) and multiply<br \/>\n\\(\\frac{35}{6}\\) X \\(\\frac{6}{7}\\)= \\(\\frac{35 X 6}{6 X 7}\\)= \\(\\frac{210}{42}\\) as both goes in 42 as 42 X 5 = 210, 42 X 1= 42,(5, 1),<br \/>\n\\(\\frac{210}{42}\\) = 5.<\/p>\n<p>Question 14.<br \/>\nHow many two and one-halves are in eight and three-fourths?<br \/>\nI have eight and three-fourths of pens with me, My friend<br \/>\nhas two and one-halves pens with him, How many more pens<br \/>\ndo I have more than my friend.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-50807\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-49.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-49\" width=\"815\" height=\"200\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-49.bmp 815w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-49-300x74.jpg 300w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-49-768x188.jpg 768w\" sizes=\"(max-width: 815px) 100vw, 815px\" \/><br \/>\n\\(\\frac{7}{2}\\) or 3\\(\\frac{1}{2}\\) two and one-halves<br \/>\nare in eight and three-fourths<br \/>\nExplanation:<br \/>\nGiven to find two and one-halves are in eight and three-fourths means<br \/>\n8\\(\\frac{3}{4}\\) \u00f7 2\\(\\frac{1}{2}\\), First we write<br \/>\n8\\(\\frac{3}{4}\\) mixed fraction as ( 8 X 4 + 3 by 4) = \\(\\frac{35}{4}\\)<br \/>\nand 2\\(\\frac{1}{2}\\) mixed fraction as (2 X 2 + 1 by 2)= \\(\\frac{5}{2}\\).<br \/>\nNow \\(\\frac{35}{4}\\) \u00f7 \\(\\frac{5}{2}\\) we write reciprocal<br \/>\nof the fraction \\(\\frac{5}{2}\\) as \\(\\frac{2}{5}\\) and multiply<br \/>\n\\(\\frac{35}{4}\\) X \\(\\frac{2}{5}\\)= \\(\\frac{35 X 2}{4 X 5}\\)= \\(\\frac{70}{20}\\) as both goes in 10 as 10 X 7 = 70, 10 X 2= 20,(7, 2),<br \/>\n\\(\\frac{70}{20}\\) = \\(\\frac{7}{2}\\) as numerator is greater<br \/>\nwe write as (3 X 2 + 1 by 2) = 3\\(\\frac{1}{2}\\).<\/p>\n<p><strong>DIVIDING WITH MIXED NUMBERS<\/strong><br \/>\n<strong>Divide. Write the answer in simplest form.<\/strong><\/p>\n<p>Question 15.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27263\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-197.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 197\" width=\"66\" height=\"44\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27263\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-197.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 197\" width=\"66\" height=\"44\" \/>= 3<br \/>\nExplanation:<br \/>\nGiven expressions as 2\\(\\frac{1}{4}\\) \u00f7 \\(\\frac{3}{4}\\),<br \/>\nFirst we write mixed fraction into fraction 2\\(\\frac{1}{4}\\) as<br \/>\n(2 X 4 + 1 by 4) = \\(\\frac{9}{4}\\), Now \\(\\frac{3}{4}\\) we<br \/>\nwrite as reciprocal and multiply \\(\\frac{4}{3}\\) as<br \/>\n\\(\\frac{9}{4}\\) X \\(\\frac{4}{3}\\) = \\(\\frac{9 X 4}{4 X 3}\\)=<br \/>\n\\(\\frac{36}{12}\\) as both goes in 12, 12 X 3 = 36,<br \/>\n12 X 1 = 12, (3, 1) = 3, therefore 2\\(\\frac{1}{4}\\) \u00f7 \\(\\frac{3}{4}\\)=<br \/>\n\\(\\frac{36}{12}\\) = 3.<\/p>\n<p>Question 16.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27159\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-198.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 198\" width=\"72\" height=\"54\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27159\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-198.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 198\" width=\"72\" height=\"54\" \/>= \\(\\frac{19}{2}\\) = 9\\(\\frac{1}{2}\\)<br \/>\nExplanation:<br \/>\nGiven expressions as 3\\(\\frac{4}{5}\\) \u00f7 \\(\\frac{2}{5}\\),<br \/>\nFirst we write mixed fraction into fraction 3\\(\\frac{4}{5}\\) as<br \/>\n(3 X 5 + 4 by 5) = \\(\\frac{19}{5}\\), Now \\(\\frac{2}{5}\\) we<br \/>\nwrite as reciprocal and multiply \\(\\frac{5}{2}\\) as<br \/>\n\\(\\frac{19}{5}\\) X \\(\\frac{5}{2}\\) = \\(\\frac{19 X 5}{5 X 2}\\)=<br \/>\n\\(\\frac{95}{10}\\) as both goes in 5, 5 X 19 = 95,<br \/>\n5 X 2 = 10, (19, 2) = \\(\\frac{19}{2}\\) as numerator is greater<br \/>\nwe write as (9 X 2 + 1 by 2)= 9\\(\\frac{1}{2}\\).<br \/>\nTherefore 3\\(\\frac{4}{5}\\) \u00f7 \\(\\frac{2}{5}\\) = \\(\\frac{19}{2}\\) = 9\\(\\frac{1}{2}\\).<\/p>\n<p>Question 17.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27264\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-199.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 199\" width=\"68\" height=\"52\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27264\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-199.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 199\" width=\"68\" height=\"52\" \/>= \\(\\frac{39}{4}\\) = 9\\(\\frac{3}{4}\\)<br \/>\nExplanation:<br \/>\nGiven expressions as 8\\(\\frac{1}{8}\\) \u00f7 \\(\\frac{5}{6}\\),<br \/>\nFirst we write mixed fraction into fraction 8\\(\\frac{1}{8}\\) as<br \/>\n(8 X 8 + 1 by 8) = \\(\\frac{65}{8}\\), Now \\(\\frac{5}{6}\\) we<br \/>\nwrite as reciprocal and multiply \\(\\frac{6}{5}\\) as<br \/>\n\\(\\frac{65}{8}\\) X \\(\\frac{6}{5}\\) = \\(\\frac{65 X 6}{8 X 5}\\) =<br \/>\n\\(\\frac{390}{40}\\) as both goes in 10, 10 X 39 = 390,<br \/>\n10 X 4 = 40, (39, 4) = \\(\\frac{39}{4}\\) as numerator is greater<br \/>\nwe write as (9 X 4 + 3 by 4)= 9\\(\\frac{3}{4}\\).<br \/>\nTherefore 8\\(\\frac{1}{8}\\) \u00f7 \\(\\frac{5}{6}\\) = \\(\\frac{39}{4}\\) = 9\\(\\frac{3}{4}\\).<\/p>\n<p>Question 18.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27265\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-200.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 200\" width=\"68\" height=\"55\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27265\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-200.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 200\" width=\"68\" height=\"55\" \/>= \\(\\frac{119}{9}\\) = 13\\(\\frac{2}{9}\\)<br \/>\nExplanation:<br \/>\nGiven expressions as 7\\(\\frac{5}{9}\\) \u00f7 \\(\\frac{4}{7}\\),<br \/>\nFirst we write mixed fraction into fraction 7\\(\\frac{5}{9}\\) as<br \/>\n(7 X 9 + 5 by 9) = \\(\\frac{68}{9}\\), Now \\(\\frac{4}{7}\\) we<br \/>\nwrite as reciprocal and multiply \\(\\frac{7}{4}\\) as<br \/>\n\\(\\frac{68}{9}\\) X \\(\\frac{7}{4}\\) = \\(\\frac{68 X 7}{9 X 4}\\) =<br \/>\n\\(\\frac{476}{36}\\) as both goes in 4, 4 X 119 = 476,<br \/>\n4 X 9 = 36, (119, 9) = \\(\\frac{119}{9}\\) as numerator is greater<br \/>\nwe write as (13 X 9 + 2 by 9)= 13\\(\\frac{2}{9}\\).<br \/>\nTherefore 7\\(\\frac{5}{9}\\) \u00f7 \\(\\frac{4}{7}\\) = \\(\\frac{119}{9}\\) = 13\\(\\frac{2}{9}\\).<\/p>\n<p>Question 19.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27266\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-201.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 201\" width=\"82\" height=\"55\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27266\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-201.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 201\" width=\"82\" height=\"55\" \/>= \\(\\frac{75}{19}\\) = 3\\(\\frac{18}{19}\\)<br \/>\nExplanation:<br \/>\nGiven expressions as 7\\(\\frac{1}{2}\\) \u00f7 1\\(\\frac{9}{10}\\),<br \/>\nFirst we write mixed fractions into fractions 7\\(\\frac{1}{2}\\) as<br \/>\n(7 X 2 + 1 by 2) = \\(\\frac{15}{2}\\), 1\\(\\frac{9}{10}\\)=<br \/>\n(1 x 10 + 9 by 10) = \\(\\frac{19}{10}\\),Now \\(\\frac{19}{10}\\) we<br \/>\nwrite as reciprocal and multiply \\(\\frac{10}{19}\\) as<br \/>\n\\(\\frac{15}{2}\\) X \\(\\frac{10}{19}\\) = \\(\\frac{15 X 10}{2 X 19}\\) =<br \/>\n\\(\\frac{150}{38}\\) as both goes in 2, 2 X 75 = 150,<br \/>\n2 X 19 = 38, (75, 19) = \\(\\frac{75}{19}\\) as numerator is greater<br \/>\nwe write as (3 X 19 + 18 by 9)= 3\\(\\frac{18}{19}\\).<br \/>\nTherefore 7\\(\\frac{1}{2}\\) \u00f7 1\\(\\frac{9}{10}\\) = \\(\\frac{75}{19}\\) = 3\\(\\frac{18}{19}\\).<\/p>\n<p>Question 20.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27160\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-202.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 202\" width=\"83\" height=\"59\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27160\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-202.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 202\" width=\"83\" height=\"59\" \/>= \\(\\frac{9}{5}\\) = 1\\(\\frac{4}{5}\\)<br \/>\nExplanation:<br \/>\nGiven expressions as 3\\(\\frac{3}{4}\\) \u00f7 2\\(\\frac{1}{12}\\),<br \/>\nFirst we write mixed fractions into fractions 3\\(\\frac{3}{4}\\) as<br \/>\n(3 X 4 + 3 by 4) = \\(\\frac{15}{4}\\), 2\\(\\frac{1}{12}\\)=<br \/>\n(2 x 12 + 1 by 12) = \\(\\frac{25}{12}\\),Now \\(\\frac{25}{12}\\) we<br \/>\nwrite as reciprocal and multiply \\(\\frac{12}{25}\\) as<br \/>\n\\(\\frac{15}{4}\\) X \\(\\frac{12}{25}\\) = \\(\\frac{15 X 12}{4 X 25}\\) =<br \/>\n\\(\\frac{180}{100}\\) as both goes in 20, 20 X 9 = 180,<br \/>\n20 X 5 = 100, (9, 5) = \\(\\frac{9}{5}\\) as numerator is greater<br \/>\nwe write as (1 X 5 + 4 by 5)= 1\\(\\frac{4}{5}\\).<br \/>\nTherefore 3\\(\\frac{3}{4}\\) \u00f7 2\\(\\frac{1}{12}\\) = \\(\\frac{9}{5}\\) = 1\\(\\frac{4}{5}\\).<\/p>\n<p>Question 21.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27280\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-203.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 203\" width=\"60\" height=\"45\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27280\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-203.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 203\" width=\"60\" height=\"45\" \/>= \\(\\frac{9}{10}\\)<br \/>\nExplanation:<br \/>\nGiven expressions as 7\\(\\frac{1}{5}\\) \u00f7 8,<br \/>\nFirst we write mixed fraction into fraction 7\\(\\frac{1}{5}\\) as<br \/>\n(7 X 5 + 1 by 5) = \\(\\frac{36}{5}\\),Now 8 we<br \/>\nwrite as reciprocal and multiply \\(\\frac{1}{8}\\) as<br \/>\n\\(\\frac{36}{5}\\) X \\(\\frac{1}{8}\\) = \\(\\frac{36 X 1}{5 X 8}\\) =<br \/>\n\\(\\frac{36}{40}\\) as both goes in 4, 4 X 9 = 36,<br \/>\n4 X 10 = 40, (9, 10) = \\(\\frac{9}{10}\\).<br \/>\nTherefore 7\\(\\frac{1}{5}\\) \u00f7 8 = \\(\\frac{9}{10}\\).<\/p>\n<p>Question 22.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27281\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-204.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 204\" width=\"69\" height=\"52\" \/>= \\(\\frac{4}{7}\\)<br \/>\nExplanation:<br \/>\nGiven expressions as 8\\(\\frac{4}{7}\\) \u00f7 15,<br \/>\nFirst we write mixed fraction into fraction 8\\(\\frac{4}{7}\\) as<br \/>\n(8 X 7 + 4 by 7) = \\(\\frac{60}{7}\\),Now 15 we<br \/>\nwrite as reciprocal and multiply \\(\\frac{1}{15}\\) as<br \/>\n\\(\\frac{60}{7}\\) X \\(\\frac{1}{15}\\) = \\(\\frac{60 X 1}{7 X 15}\\) =<br \/>\n\\(\\frac{60}{105}\\) as both goes in 15, 15 X 4 = 60,<br \/>\n15 X 7 = 105, (4, 7) = \\(\\frac{4}{7}\\).<br \/>\nTherefore 8\\(\\frac{4}{7}\\) \u00f7 15 = \\(\\frac{4}{7}\\).<\/p>\n<p>Question 23.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27282\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-205.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 205\" width=\"68\" height=\"49\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27282\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-205.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 205\" width=\"68\" height=\"49\" \/>= \\(\\frac{25}{2}\\) = 12\\(\\frac{1}{2}\\)<br \/>\nExplanation:<br \/>\nGiven expressions as 8\\(\\frac{1}{3}\\) \u00f7 \\(\\frac{2}{3}\\),<br \/>\nFirst we write mixed fraction into fraction 8\\(\\frac{1}{3}\\) as<br \/>\n(8 X 3 + 1 by 3) = \\(\\frac{25}{3}\\),Now \\(\\frac{2}{3}\\) we<br \/>\nwrite as reciprocal and multiply \\(\\frac{3}{2}\\) as<br \/>\n\\(\\frac{25}{3}\\) X \\(\\frac{3}{2}\\) = \\(\\frac{25 X 3}{3 X 2}\\) =<br \/>\n\\(\\frac{75}{6}\\) as both goes in 3, 3 X 25 = 75,<br \/>\n3 X 2 = 6, (25, 2) = \\(\\frac{25}{2}\\) as numerator is greater<br \/>\nwe write as (12 X 2 + 1 by 2)= 12\\(\\frac{1}{2}\\).<br \/>\nTherefore 8\\(\\frac{1}{3}\\) \u00f7 \\(\\frac{2}{3}\\) = \\(\\frac{25}{2}\\) = 12\\(\\frac{1}{2}\\).<\/p>\n<p>Question 24.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27283\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-206.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 206\" width=\"61\" height=\"51\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27283\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-206.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 206\" width=\"61\" height=\"51\" \/>= 11<br \/>\nExplanation:<br \/>\nGiven expressions as 9\\(\\frac{1}{6}\\) \u00f7 \\(\\frac{5}{6}\\),<br \/>\nFirst we write mixed fraction into fraction 9\\(\\frac{1}{6}\\) as<br \/>\n(9 X 6 + 1 by 6) = \\(\\frac{55}{6}\\),Now \\(\\frac{5}{6}\\) we<br \/>\nwrite as reciprocal and multiply \\(\\frac{6}{5}\\) as<br \/>\n\\(\\frac{55}{6}\\) X \\(\\frac{6}{5}\\) = \\(\\frac{55 X 6}{6 X 5}\\) =<br \/>\n\\(\\frac{330}{30}\\) as both goes in 30, 30 X 11 = 330,<br \/>\n3 X 1 = 30, (11, 1) = \\(\\frac{330}{30}\\) = 11,<br \/>\nTherefore 9\\(\\frac{1}{6}\\) \u00f7 \\(\\frac{5}{6}\\) = 11.<\/p>\n<p>Question 25.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27284\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-207.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 207\" width=\"79\" height=\"56\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27284\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-207.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 207\" width=\"79\" height=\"56\" \/>= \\(\\frac{6}{5}\\) = 1\\(\\frac{1}{5}\\)<br \/>\nExplanation:<br \/>\nGiven expressions as 13 \u00f7\u00a0 10\\(\\frac{5}{6}\\)<br \/>\nFirst we write mixed fraction into fraction 10\\(\\frac{5}{6}\\) as<br \/>\n(10 X 6 + 5 by 6) = \\(\\frac{65}{6}\\),Now \\(\\frac{65}{6}\\) we<br \/>\nwrite as reciprocal and multiply \\(\\frac{6}{65}\\) as<br \/>\n13 X \\(\\frac{6}{65}\\) = \\(\\frac{13 X 6}{1 X 65}\\) =<br \/>\n\\(\\frac{78}{65}\\) as both goes in 13, 13 X 6 = 78,<br \/>\n13 X 5 = 65, (6, 5) = \\(\\frac{6}{5}\\) as numerator is greater<br \/>\nwe write as (1 X 5 + 1 by 5)= 1\\(\\frac{1}{5}\\).<br \/>\nTherefore 13 \u00f7\u00a0 10\\(\\frac{5}{6}\\) = \\(\\frac{6}{5}\\) = 1\\(\\frac{1}{5}\\).<\/p>\n<p>Question 26.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27285\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-208.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 208\" width=\"68\" height=\"48\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27285\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-208.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 208\" width=\"68\" height=\"48\" \/>= \\(\\frac{33}{16}\\) = 2\\(\\frac{1}{16}\\)<\/p>\n<p>Explanation:<br \/>\nGiven expressions as 12 \u00f7 5\\(\\frac{9}{11}\\)<br \/>\nFirst we write mixed fraction into fraction 5\\(\\frac{9}{11}\\) as<br \/>\n(5 X 11 + 9 by 11) = \\(\\frac{64}{11}\\),Now \\(\\frac{65}{11}\\) we<br \/>\nwrite as reciprocal and multiply \\(\\frac{11}{64}\\) as<br \/>\n12 X \\(\\frac{11}{64}\\) = \\(\\frac{12 X 11}{1 X 64}\\) =<br \/>\n\\(\\frac{132}{64}\\) as both goes in 4, 4 X 33 = 132,<br \/>\n4 X 16 = 64, (33, 16) = \\(\\frac{33}{16}\\) as numerator is greater<br \/>\nwe write as (2 X 16 + 1 by 16)= 2\\(\\frac{1}{16}\\).<br \/>\nTherefore 12 \u00f7 5\\(\\frac{9}{11}\\) = \\(\\frac{33}{16}\\) = 2\\(\\frac{1}{16}\\).<\/p>\n<p>Question 27.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27286\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-209.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 209\" width=\"71\" height=\"55\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27286\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-209.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 209\" width=\"71\" height=\"55\" \/>= \\(\\frac{2}{7}\\)<\/p>\n<p>Explanation:<br \/>\nGiven expressions as \\(\\frac{7}{8}\\) \u00f7 3\\(\\frac{1}{16}\\),<br \/>\nFirst we write mixed fraction into fraction 3\\(\\frac{1}{16}\\) as<br \/>\n(3 X 16 + 1 by 16) = \\(\\frac{49}{16}\\),Now \\(\\frac{49}{16}\\) we<br \/>\nwrite as reciprocal and multiply \\(\\frac{16}{49}\\) as<br \/>\n\\(\\frac{7}{8}\\) X \\(\\frac{16}{49}\\) = \\(\\frac{7 X 16}{8 X 49}\\) =<br \/>\n\\(\\frac{112}{392}\\) as both goes in 56, 56 X 2 = 112,<br \/>\n56 X 7 = 392, (2, 7) = \\(\\frac{2}{7}\\),<br \/>\nTherefore \\(\\frac{7}{8}\\) \u00f7 3\\(\\frac{1}{16}\\) = \\(\\frac{2}{7}\\).<\/p>\n<p>Question 28.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27287\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-210.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 210\" width=\"71\" height=\"49\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27287\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-210.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 210\" width=\"71\" height=\"49\" \/>= \\(\\frac{10}{33}\\)<\/p>\n<p>Explanation:<br \/>\nGiven expressions as \\(\\frac{4}{9}\\) \u00f7 1\\(\\frac{7}{15}\\),<br \/>\nFirst we write mixed fraction into fraction 1\\(\\frac{7}{15}\\) as<br \/>\n(1 X 15 + 7 by 15) = \\(\\frac{22}{15}\\),Now \\(\\frac{22}{15}\\) we<br \/>\nwrite as reciprocal and multiply \\(\\frac{15}{22}\\) as<br \/>\n\\(\\frac{4}{9}\\) X \\(\\frac{15}{22}\\) = \\(\\frac{4 X 15}{9 X 22}\\) =<br \/>\n\\(\\frac{60}{198}\\) as both goes in 6, 6 X 10 = 60,<br \/>\n6 X 33 = 198, (10, 33) = \\(\\frac{10}{33}\\), therefore<br \/>\n\\(\\frac{4}{9}\\) \u00f7 1\\(\\frac{7}{15}\\) = \\(\\frac{10}{33}\\).<\/p>\n<p>Question 29.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27267\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-211.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 211\" width=\"77\" height=\"63\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27267\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-211.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 211\" width=\"77\" height=\"63\" \/>= \\(\\frac{23}{18}\\) or 1\\(\\frac{5}{18}\\)<br \/>\nExplanation:<br \/>\nGiven expressions as 4\\(\\frac{5}{16}\\) \u00f7 3\\(\\frac{3}{8}\\),<br \/>\nFirst we write mixed fractions into fractions as 4\\(\\frac{5}{16}\\) =<br \/>\n(4 X 16 + 5 by 16) = \\(\\frac{69}{16}\\) and 3\\(\\frac{3}{8}\\) =<br \/>\n(3 X 8 + 3 by 8) = \\(\\frac{27}{8}\\), Now we write<br \/>\n\\(\\frac{69}{16}\\) \u00f7 \\(\\frac{27}{8}\\) now reciprocal of<br \/>\nthe fraction \\(\\frac{27}{8}\\) as \\(\\frac{8}{27}\\) and<br \/>\nmultiply as \\(\\frac{69}{16}\\) X \\(\\frac{8}{27}\\) =<br \/>\n\\(\\frac{69 X 8}{16 X 27}\\) = \\(\\frac{552}{432}\\),<br \/>\nwe can further simplify as both goes in 24, 24 X 23 = 552 and 24 X 18 = 432,<br \/>\n(23,18)=\\(\\frac{23}{18}\\) as numerator is greater<br \/>\nwe write as (1 X 18 + 5 by 18) = 1\\(\\frac{5}{18}\\).<br \/>\nTherefore 4\\(\\frac{5}{16}\\) \u00f7 3\\(\\frac{3}{8}\\) = \\(\\frac{23}{18}\\) or 1\\(\\frac{5}{18}\\).<\/p>\n<p>Question 30.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27288\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-212.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 212\" width=\"70\" height=\"54\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27288\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-212.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 212\" width=\"70\" height=\"54\" \/>= \\(\\frac{16}{15}\\) or 1\\(\\frac{1}{15}\\)<br \/>\nExplanation:<br \/>\nGiven expressions as 6\\(\\frac{2}{9}\\) \u00f7 5\\(\\frac{5}{9}\\),<br \/>\nFirst we write mixed fractions into fractions as 6\\(\\frac{2}{9}\\) =<br \/>\n(6 X 9 + 2 by 9) = \\(\\frac{56}{9}\\) and 5\\(\\frac{5}{6}\\) =<br \/>\n(5 X 6 + 5 by 6) = \\(\\frac{35}{6}\\), Now we write<br \/>\n\\(\\frac{56}{9}\\) \u00f7 \\(\\frac{35}{6}\\) now reciprocal of<br \/>\nthe fraction \\(\\frac{35}{6}\\) as \\(\\frac{6}{35}\\) and<br \/>\nmultiply as \\(\\frac{56}{9}\\) X \\(\\frac{6}{35}\\) =<br \/>\n\\(\\frac{56 X 6}{9 X 35}\\) = \\(\\frac{336}{315}\\),<br \/>\nwe can further simplify as both goes in 21, 21 X 16 = 336 and 21 X 15 = 315,<br \/>\n(16,15)=\\(\\frac{16}{15}\\) as numerator is greater<br \/>\nwe write as (1 X 15 + 1 by 15) = 1\\(\\frac{1}{15}\\), therefore<br \/>\n6\\(\\frac{2}{9}\\) \u00f7 5\\(\\frac{5}{9}\\) = \\(\\frac{16}{15}\\) or 1\\(\\frac{1}{15}\\).<\/p>\n<p>Question 31.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend \ufb01nds the quotient of 3\\(\\frac{1}{2}\\) and 1\\(\\frac{2}{3}\\). Is your friend correct? Explain your reasoning.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27289\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-213.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 213\" width=\"386\" height=\"68\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-213.png 386w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-213-300x53.png 300w\" sizes=\"(max-width: 386px) 100vw, 386px\" \/><br \/>\nNo, Friend is in correct, As 3\\(\\frac{1}{2}\\) \u00f7 1\\(\\frac{2}{3}\\) =<br \/>\n\\(\\frac{21}{10}\\) or 2\\(\\frac{1}{10}\\) \u2260 8\\(\\frac{3}{4}\\)<\/p>\n<p>Explanation:<br \/>\nGiven expressions are 3\\(\\frac{1}{2}\\) \u00f7 1\\(\\frac{2}{3}\\),<br \/>\nFirst we write mixed fractions into fractions as 3\\(\\frac{1}{2}\\) =<br \/>\n(3 X 2 + 1 by 2) = \\(\\frac{7}{2}\\) and 1\\(\\frac{2}{3}\\) =<br \/>\n(1 X 3 + 2 by 3) = \\(\\frac{5}{3}\\), Now we write<br \/>\n\\(\\frac{7}{2}\\) \u00f7 \\(\\frac{5}{3}\\) now reciprocal of<br \/>\nthe fraction \\(\\frac{5}{3}\\) as \\(\\frac{3}{5}\\) and<br \/>\nmultiply as \\(\\frac{7}{2}\\) X \\(\\frac{3}{5}\\) =<br \/>\n\\(\\frac{7 X 3}{2 X 5}\\) = \\(\\frac{21}{10}\\),<br \/>\nas numerator is greater we write as (2 X 10 + 1 by 10) = 2\\(\\frac{1}{10}\\), therefore<br \/>\n3\\(\\frac{1}{2}\\) \u00f7 1\\(\\frac{2}{3}\\) = \\(\\frac{21}{10}\\) or<br \/>\n2\\(\\frac{1}{10}\\) \u2260 8\\(\\frac{3}{4}\\) so friend is incorrect.<\/p>\n<p>Question 32.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nA platinum nugget weighs 3\\(\\frac{1}{2}\\) ounces. How many \\(\\frac{1}{4}\\) ounce pieces can be cut from the nugget?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27290\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-214.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 214\" width=\"196\" height=\"186\" \/><br \/>\n14 pieces of \\(\\frac{1}{4}\\) ounce can be cut from the nugget<br \/>\nwhich weighs 3\\(\\frac{1}{2}\\) ounces<\/p>\n<p>Explanation:<br \/>\nGiven a platinum nugget weighs 3\\(\\frac{1}{2}\\) ounces,<br \/>\nnumber of pieces of \\(\\frac{1}{4}\\) ounce pieces can be<br \/>\ncut from the nugget are 3\\(\\frac{1}{2}\\) \u00f7 \\(\\frac{1}{4}\\) =<br \/>\nFirst we write mixed fraction into fraction as 3\\(\\frac{1}{2}\\) =<br \/>\n(3 X 2 + 1 by 2) = \\(\\frac{7}{2}\\), Now<br \/>\n\\(\\frac{7}{2}\\) \u00f7 \\(\\frac{1}{4}\\) now reciprocal of<br \/>\nthe fraction \\(\\frac{1}{4}\\) as \\(\\frac{4}{1}\\) and<br \/>\nmultiply as \\(\\frac{7}{2}\\) X \\(\\frac{4}{1}\\) =<br \/>\n\\(\\frac{7 X 4}{2 X 1}\\) = \\(\\frac{28}{2}\\),we can further simplify<br \/>\nas both goes in 2, 2 X 14 = 28 and 2 X 1 = 2, (14,1)= 14, therefore<br \/>\n14 pieces of \\(\\frac{1}{4}\\) ounce can be cut from the nugget<br \/>\nwhich weighs 3\\(\\frac{1}{2}\\) ounces.<\/p>\n<p><strong>ORDER OF OPERATIONS<\/strong><br \/>\n<strong>Evaluate the expression. Write the answer in simplest form.<\/strong><\/p>\n<p>Question 33.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27291\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-215.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 215\" width=\"89\" height=\"48\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27291\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-215.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 215\" width=\"89\" height=\"48\" \/>= 3<br \/>\nExplanation:<br \/>\nGiven expression as (3 \u00f7 1\\(\\frac{1}{5}\\))+ \\(\\frac{1}{2}\\)<br \/>\nFirst we write mixed fraction into fraction as 1\\(\\frac{1}{5}\\) =<br \/>\n(1 X 5 + 1 by 5) = \\(\\frac{6}{5}\\) Now we calculate first<br \/>\n3 \u00f7 \\(\\frac{6}{5}\\)\u00a0 now reciprocal of<br \/>\nthe fraction \\(\\frac{6}{5}\\) as \\(\\frac{5}{6}\\) and<br \/>\nmultiply as 3 X \\(\\frac{5}{6}\\) =<br \/>\n\\(\\frac{3 X 5}{1 X 6}\\) = \\(\\frac{15}{6}\\),as both goes in 3,<br \/>\n3 X 5 = 15 and 3 X 2 = 6, (5,2)= \\(\\frac{5}{2}\\), now we add with<br \/>\n\\(\\frac{1}{2}\\), \\(\\frac{5}{2}\\) + \\(\\frac{1}{2}\\) as<br \/>\nboth have same denominators we add numerators as (5 + 1) and write as<br \/>\n\\(\\frac{6}{2}\\) now as both goes in 2, 2 X 3 = 6, 2 X 1 = 2, (3,1) = 3,<br \/>\ntherefore (3 \u00f7 1\\(\\frac{1}{5}\\))+ \\(\\frac{1}{2}\\) = 3.<\/p>\n<p>Question 34.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27292\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-216.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 216\" width=\"94\" height=\"44\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27292\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-216.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 216\" width=\"94\" height=\"44\" \/>= \\(\\frac{5}{3}\\) = 1\\(\\frac{2}{3}\\)<\/p>\n<p>Given expression as (4\\(\\frac{2}{3}\\) &#8211; 1\\(\\frac{1}{3}\\)) \u00f7 2<br \/>\nFirst we write mixed fractions into fractions as 4\\(\\frac{2}{3}\\) =<br \/>\n(4 X 3 + 2 by 3) = \\(\\frac{14}{3}\\) and 1\\(\\frac{1}{3}\\) =<br \/>\n(1 X 3 + 1 by 3) = \\(\\frac{4}{3}\\), Now first we calculate<br \/>\n\\(\\frac{14}{3}\\) &#8211; \\(\\frac{4}{3}\\)\u00a0 as denominators are same<br \/>\nnumerators become (14 &#8211; 4 ) = 10, we get \u00a0\\(\\frac{10}{3}\\)<br \/>\nnow \\(\\frac{10}{3}\\)\u00a0 \u00f7 2 we write 2<br \/>\nas reciprocal and multiply \\(\\frac{10}{3}\\) X \\(\\frac{1}{2}\\) =<br \/>\n\\(\\frac{10 X 1}{3 X 2}\\) = \\(\\frac{10}{6}\\),<br \/>\nwe can further simplify as both goes in 2, 2 X 5 = 10 and 2 X 3 = 6,<br \/>\n(5,3)=\\(\\frac{5}{3}\\) as numerator is greater<br \/>\nwe write as (1 X 3 + 2 by 3) = 1\\(\\frac{2}{3}\\), therefore<br \/>\n(4\\(\\frac{2}{3}\\) &#8211; 1\\(\\frac{1}{3}\\)) \u00f7 2 = \\(\\frac{5}{3}\\) or 1\\(\\frac{2}{3}\\).<\/p>\n<p>Question 35.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27293\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-217.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 217\" width=\"95\" height=\"49\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27293\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-217.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 217\" width=\"95\" height=\"49\" \/>= 3<br \/>\nExplanation<br \/>\nGiven expression as \\(\\frac{2}{5}\\) + (2\\(\\frac{1}{6}\\) \u00f7 \\(\\frac{1}{6}\\)) First we write mixed fraction into fraction as 2\\(\\frac{1}{6}\\) =<br \/>\n(2 X 6 + 1 by 6) = \\(\\frac{13}{6}\\),Now first we calculate<br \/>\n\\(\\frac{13}{6}\\) \u00f7 \\(\\frac{5}{6}\\)\u00a0 we write \\(\\frac{5}{6}\\)<br \/>\nas reciprocal and multiply \\(\\frac{13}{6}\\) X \\(\\frac{6}{5}\\) =<br \/>\n\\(\\frac{13 X 6}{6 X 5}\\) = \\(\\frac{78}{30}\\),<br \/>\nwe can further simplify as both goes in 6, 6 X 13 = 78 and 6 X 5 = 30,<br \/>\n(13,5)=\\(\\frac{13}{5}\\), Now we add as<br \/>\n\\(\\frac{2}{5}\\) + \\(\\frac{13}{5}\\) as both have same denominators we add numerators and write as \\(\\frac{15}{5}\\), now as both goes in 5,<br \/>\n5 X 3= 15, 5 X 1 = 5, (3, 1) = 3, therefore \\(\\frac{2}{5}\\) +<br \/>\n(2\\(\\frac{1}{6}\\) \u00f7 \\(\\frac{1}{6}\\)) = 3.<\/p>\n<p>Question 36.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27268\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-218.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 218\" width=\"104\" height=\"52\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27268\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-218.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 218\" width=\"104\" height=\"52\" \/>= \\(\\frac{4}{3}\\) or 1\\(\\frac{1}{3}\\)<br \/>\nExplanation:<br \/>\nGiven expression as (5\\(\\frac{5}{6}\\) \u00f7 3\\(\\frac{3}{4}\\)) &#8211; \\(\\frac{2}{9}\\),First we write mixed fractions into fractions as 5\\(\\frac{5}{6}\\) =<br \/>\n(5 X 6 + 5 by 6) = \\(\\frac{35}{6}\\) and 3\\(\\frac{3}{4}\\)=<br \/>\n(3 X 4 + 3 by 4) = \\(\\frac{15}{4}\\). Now first we calculate<br \/>\n\\(\\frac{35}{6}\\) \u00f7 \\(\\frac{15}{4}\\)\u00a0 we write \\(\\frac{15}{4}\\)<br \/>\nas reciprocal and multiply \\(\\frac{35}{6}\\) X \\(\\frac{4}{15}\\) =<br \/>\n\\(\\frac{35 X 4}{6 X 15}\\) = \\(\\frac{140}{90}\\),<br \/>\nwe can further simplify as both goes in 10, 10 X 14 = 140 and 10 X 9 = 90,<br \/>\n(14,9)=\\(\\frac{14}{9}\\), Now we subtract as \\(\\frac{14}{9}\\) &#8211; \\(\\frac{2}{9}\\) as both have same denominators are same we subtract numerators and write as<br \/>\n\\(\\frac{12}{9}\\) now as both goes in 3,<br \/>\n3 X 4= 12, 3 X 3 = 9, (4, 3) = \\(\\frac{4}{3}\\) as numerator is greater<br \/>\nwe write as (1 X 3 + 1 by 3), Therefore (5\\(\\frac{5}{6}\\) \u00f7 3\\(\\frac{3}{4}\\)) &#8211; \\(\\frac{2}{9}\\) = \\(\\frac{4}{3}\\) or 1\\(\\frac{1}{3}\\).<\/p>\n<p>Question 37.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27294\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-219.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 219\" width=\"105\" height=\"54\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27294\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-219.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 219\" width=\"105\" height=\"54\" \/>= \\(\\frac{165}{26}\\) or 6\\(\\frac{9}{26}\\)<br \/>\nExplanation:<br \/>\nGiven expression as 6\\(\\frac{1}{2}\\) &#8211; (\\(\\frac{7}{8}\\) \u00f7 5\\(\\frac{11}{16}\\)), First we write mixed fraction into fraction as 5\\(\\frac{11}{16}\\) =<br \/>\n(5 X 16 + 11 by 16) = \\(\\frac{91}{16}\\), Now first we calculate<br \/>\n\\(\\frac{7}{8}\\) \u00f7 \\(\\frac{91}{16}\\), we write \\(\\frac{91}{16}\\)<br \/>\nas reciprocal and multiply \\(\\frac{7}{8}\\) X \\(\\frac{16}{91}\\) =<br \/>\n\\(\\frac{7 X 16}{8 X 91}\\) = \\(\\frac{112}{728}\\),<br \/>\nwe can further simplify as both goes in 28, 28 X 4 = 112 and 28 X 26 = 728,<br \/>\n(4,26)=\\(\\frac{4}{26}\\), We write mixed fraction into fraction of 6\\(\\frac{1}{2}\\) as (6 X 2 + 1 by 2) = \\(\\frac{13}{2}\\) Now we subtract as \\(\\frac{13}{2}\\) &#8211; \\(\\frac{4}{26}\\) as both should have same denominator we multiply numerator and denominator by 13 for \\(\\frac{13}{2}\\) X \\(\\frac{13}{13}\\) =<br \/>\n\\(\\frac{13 X 13}{2 X 13}\\) = \\(\\frac{169}{26}\\) now we subtract as<br \/>\n\\(\\frac{169}{26}\\) &#8211; \\(\\frac{4}{26}\\)as denominators are same we<br \/>\nsubtract numerators (169 &#8211; 4 ) and write as \\(\\frac{165}{26}\\),<br \/>\nas numerator is greater we write as (6 X 26 + 9 by 26) = 6\\(\\frac{9}{26}\\).<br \/>\nTherefore 6\\(\\frac{1}{2}\\) &#8211; (\\(\\frac{7}{8}\\) \u00f7 5\\(\\frac{11}{16}\\)) =<br \/>\n\\(\\frac{165}{26}\\) or 6\\(\\frac{9}{26}\\).<\/p>\n<p>Question 38.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27269\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-220.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 220\" width=\"104\" height=\"54\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27269\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-220.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 220\" width=\"104\" height=\"54\" \/>= \\(\\frac{11}{10}\\) or 1\\(\\frac{1}{10}\\)<br \/>\nExplanation:<br \/>\nGiven expression as 9\\(\\frac{1}{6}\\) \u00f7 (5 + 3\\(\\frac{1}{3}\\)),<br \/>\nFirst we write mixed fraction into fraction for 3\\(\\frac{1}{3}\\) as<br \/>\n(3 X 3 + 1 by 3) = \\(\\frac{10}{3}\\), Now first we calculate<br \/>\n5 + \\(\\frac{10}{3}\\) as (5 X 3 +10 by 3) = \\(\\frac{25}{3}\\),<br \/>\nWe write mixed fraction into fraction of 9\\(\\frac{1}{6}\\)<br \/>\nas (9 X 6 + 1 by 6) = \\(\\frac{55}{6}\\) now we divide with \\(\\frac{25}{3}\\),<br \/>\nnow we write as reciprocal and multiply \\(\\frac{55}{6}\\) X \\(\\frac{3}{25}\\) =<br \/>\n\\(\\frac{55 X 3}{6 X 25}\\) = \\(\\frac{165}{150}\\),<br \/>\nwe can further simplify as both goes in 15, 15 X 11 = 165 and 15 X 10 = 150,<br \/>\n(11,10)=\\(\\frac{11}{10}\\), as numerator is greater we write as<br \/>\n(1 X 10 + 1 by 10) = 1\\(\\frac{1}{10}\\). Therefore 9\\(\\frac{1}{6}\\) \u00f7<br \/>\n(5 + 3\\(\\frac{1}{3}\\)) = \\(\\frac{11}{10}\\) or 1\\(\\frac{1}{<br \/>\n10}\\).<\/p>\n<p>Question 39.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27270\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-221.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 221\" width=\"105\" height=\"48\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27270\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-221.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 221\" width=\"105\" height=\"48\" \/>= \\(\\frac{66}{5}\\) or 13\\(\\frac{1}{5}\\)<\/p>\n<p>Given expression as 3\\(\\frac{3}{5}\\) + (4\\(\\frac{4}{15}\\) \u00f7<br \/>\n\\(\\frac{4}{9}\\)), First we write mixed fraction into fraction<br \/>\nfor 4\\(\\frac{4}{15}\\) as<br \/>\n(4 X 15 + 4 by 15) = \\(\\frac{64}{15}\\), Now first we calculate<br \/>\n\\(\\frac{64}{15}\\) \u00f7 \\(\\frac{4}{9}\\)now we write as reciprocal<br \/>\nand multiply \\(\\frac{64}{15}\\) X \\(\\frac{9}{4}\\) =<br \/>\n\\(\\frac{64 X 9}{15 X 4}\\) = \\(\\frac{576}{60}\\),<br \/>\nwe can further simplify as both goes in 12, 12 X 48 = 576 and 12 X 5 = 60,<br \/>\n(48, 5)=\\(\\frac{48}{5}\\), we write mixed fraction into fraction for<br \/>\n3\\(\\frac{3}{5}\\) as (3 X 5 + 3 by 5) = \\(\\frac{18}{5}\\)<br \/>\nNow \\(\\frac{18}{5}\\) + \\(\\frac{48}{5}\\)\u00a0 as both have<br \/>\nsame denominators we add numerators and write as \\(\\frac{66}{5}\\)<br \/>\nas numerator is greater we write as (13 X 5 + 1 by 5) = 13\\(\\frac{1}{5}\\).<br \/>\nTherefore 3\\(\\frac{3}{5}\\) + (4\\(\\frac{4}{15}\\) \u00f7 \\(\\frac{4}{9}\\)) =<br \/>\n\\(\\frac{66}{5}\\) or 13\\(\\frac{1}{5}\\).<\/p>\n<p>Question 40.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27161\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-222.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 222\" width=\"103\" height=\"50\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27161\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-222.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 222\" width=\"103\" height=\"50\" \/>= \\(\\frac{7}{54}\\)<\/p>\n<p>Given expression as (\\(\\frac{3}{5}\\) X \\(\\frac{7}{12}\\)) \u00f7<br \/>\n2\\(\\frac{7}{10}\\), First we multiply \\(\\frac{3}{5}\\) X<br \/>\n\\(\\frac{7}{12}\\) = \\(\\frac{3 X 7}{5 X 12}\\) = \\(\\frac{21}{60}\\),<br \/>\nwe can further simplify as both goes in 3, 3 X 7 = 21 and 3 X 20 = 60,<br \/>\n(7, 20)=\\(\\frac{7}{20}\\), Now we have \\(\\frac{7}{20}\\) \u00f7 2\\(\\frac{7}{10}\\), we write mixed fraction into fraction for 2\\(\\frac{7}{10}\\) as<br \/>\n(2 X 10 + 7 by 10) = \\(\\frac{27}{10}\\) now we write reciprocal<br \/>\nand multiply \\(\\frac{7}{20}\\) X \\(\\frac{10}{27}\\) =<br \/>\n\\(\\frac{7 X 10}{20 X 27}\\) = \\(\\frac{70}{540}\\) as both goes in 10,<br \/>\n10 X 7 = 70 and 10 X 54 = 540, (7,54) =\u00a0 \\(\\frac{7}{54}\\), Therefore<br \/>\n(\\(\\frac{3}{5}\\) X \\(\\frac{7}{12}\\)) \u00f7 2\\(\\frac{7}{10}\\) = \\(\\frac{7}{54}\\).<\/p>\n<p>Question 41.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27271\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-223.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 223\" width=\"89\" height=\"51\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27271\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-223.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 223\" width=\"89\" height=\"51\" \/>= \\(\\frac{10}{3}\\) or 3\\(\\frac{1}{3}\\)<\/p>\n<p>Explanation:<br \/>\nGiven expression as (4\\(\\frac{3}{8}\\) \u00f7 \\(\\frac{3}{4}\\)) X \\(\\frac{4}{7}\\), First we write mixed fraction into fraction for 4\\(\\frac{3}{8}\\) as<br \/>\n(4 X 8 + 3 by 8) = \\(\\frac{35}{8}\\), now we divide with \\(\\frac{3}{4}\\),<br \/>\nnow we write as reciprocal and multiply \\(\\frac{35}{8}\\) X \\(\\frac{4}{3}\\) =<br \/>\n\\(\\frac{35 X 4}{8 X 3}\\) = \\(\\frac{140}{24}\\),<br \/>\nwe can further simplify as both goes in 4, 4 X 35 = 140 and 4 X 6 = 24,<br \/>\n(35,6)=\\(\\frac{35}{6}\\), now we multiply with \\(\\frac{35}{6}\\) X \\(\\frac{4}{7}\\) = \\(\\frac{35 X 4}{6 X 7}\\) = \\(\\frac{140}{42}\\),<br \/>\nas both goes in 14, 14 X 10 = 140, 14 X 3 = 42, (10, 3) = \\(\\frac{10}{3}\\),<br \/>\nas numerator is greater we write (3 X 3 + 1 by 3) = 3\\(\\frac{1}{3}\\),<br \/>\ntherefore (4\\(\\frac{3}{8}\\) \u00f7 \\(\\frac{3}{4}\\)) X \\(\\frac{4}{7}\\) =<br \/>\n\\(\\frac{10}{3}\\) or 3\\(\\frac{1}{3}\\).<\/p>\n<p>Question 42.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27295\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-224.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 224\" width=\"109\" height=\"50\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27295\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-224.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 224\" width=\"109\" height=\"50\" \/>= \\(\\frac{25}{2}\\) = 12\\(\\frac{1}{2}\\)<br \/>\nExplanation:<br \/>\nGiven expression as (1\\(\\frac{9}{11}\\) X 4\\(\\frac{7}{12}\\)) \u00f7 \\(\\frac{2}{3}\\), First we write mixed fraction into fraction for 1\\(\\frac{9}{11}\\) as<br \/>\n(1 X 11 + 9 by 11) = \\(\\frac{20}{11}\\) and 4\\(\\frac{7}{12}\\) as<br \/>\n(4 X 12 + 7 by 12) = \\(\\frac{55}{12}\\) now we calculate first<br \/>\n\\(\\frac{20}{11}\\) X \\(\\frac{55}{12}\\) = \\(\\frac{20 X 55}{11 X 12}\\) =<br \/>\n\\(\\frac{1100}{132}\\) we further simply as both goes in 44,<br \/>\n44 X 25 = 1100, 44 X 3 = 132, (25, 3) = \\(\\frac{25}{3}\\),<br \/>\nNow we calculate as \\(\\frac{25}{3}\\) \u00f7 \\(\\frac{2}{3}\\)<br \/>\nnow we write as reciprocal and multiply \\(\\frac{25}{3}\\) X \\(\\frac{3}{2}\\) =<br \/>\n\\(\\frac{25 X 3}{3 X 2}\\) = \\(\\frac{75}{6}\\), as both goes in 3,<br \/>\n3 X 25 = 75, 3 X 2 = 6, (25, 2) = \\(\\frac{25}{2}\\)<br \/>\nas numerator is greater we write (12 X 2 + 1 by 2) = 12\\(\\frac{1}{2}\\),<br \/>\ntherefore (1\\(\\frac{9}{11}\\) X 4\\(\\frac{7}{12}\\)) \u00f7 \\(\\frac{2}{3}\\) =<br \/>\n\\(\\frac{25}{2}\\) = 12\\(\\frac{1}{2}\\).<\/p>\n<p>Question 43.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27296\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-225.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 225\" width=\"117\" height=\"55\" \/><br \/>\n<img decoding=\"async\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-225.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 225\" \/>= \\(\\frac{7}{108}\\)<\/p>\n<p>Explanation:<br \/>\nGiven expression as 3\\(\\frac{4}{15}\\) \u00f7 (8 X 6\\(\\frac{3}{10}\\)),<br \/>\nFirst we write mixed fraction into fraction for 6\\(\\frac{3}{10}\\) as<br \/>\n(6 X 10 + 3 by 10) = \\(\\frac{63}{10}\\) now we calculate first<br \/>\n8 X \\(\\frac{63}{10}\\) = \\(\\frac{8 X 63}{10}\\) =<br \/>\n\\(\\frac{504}{10}\\) we further simply as both goes in 2,<br \/>\n2 X 252 = 504, 2 X 5 = 10, (252, 5) = \\(\\frac{252}{5}\\),<br \/>\nNow 3\\(\\frac{4}{15}\\) = ( 3 X 15 + 4 by 15) = \\(\\frac{49}{15}\\)<br \/>\nNow we calculate as \\(\\frac{49}{15}\\) \u00f7 \\(\\frac{252}{5}\\)<br \/>\nnow we write as reciprocal and multiply \\(\\frac{49}{15}\\) X \\(\\frac{5}{252}\\) =<br \/>\n\\(\\frac{49 X 5}{15 X 252}\\) = \\(\\frac{245}{3780}\\), as both goes in 35,<br \/>\n35 X 7 = 245, 35 X 108 = 3780, (7, 108) = \\(\\frac{7}{108}\\).<br \/>\nTherefore 3\\(\\frac{4}{15}\\) \u00f7 (8 X 6\\(\\frac{3}{10}\\)) = \\(\\frac{7}{108}\\).<\/p>\n<p>Question 44.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27297\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-226.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 226\" width=\"124\" height=\"56\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27297\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-226.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 226\" width=\"124\" height=\"56\" \/>= \\(\\frac{11}{35}\\)<\/p>\n<p>Explanation:<br \/>\nGiven expression as 2\\(\\frac{5}{14}\\) \u00f7 (2\\(\\frac{5}{8}\\) X<br \/>\n1\\(\\frac{3}{7}\\)),First we write mixed fraction into fraction<br \/>\nfor 2\\(\\frac{5}{8}\\) as<br \/>\n(2 X 8 + 5 by 8) = \\(\\frac{21}{8}\\) and 1\\(\\frac{3}{7}\\) =<br \/>\n(1 X 7 + 3 by 7) = \\(\\frac{10}{7}\\) now we calculate first<br \/>\n\\(\\frac{21}{8}\\) X \\(\\frac{10}{7}\\) = \\(\\frac{21 X 10}{8 X 7}\\) =<br \/>\n\\(\\frac{210}{56}\\) we further simply as both goes in 2,<br \/>\n2 X 105 = 210, 2 X 28 = 56, (105, 28) = \\(\\frac{105}{28}\\),<br \/>\nwe write mixed fraction as fraction 2\\(\\frac{5}{14}\\) as<br \/>\n(2 X 14 + 5 by 14) = \\(\\frac{33}{14}\\),Now we calculate as<br \/>\n\\(\\frac{33}{14}\\) \u00f7 \\(\\frac{105}{28}\\), now we write as reciprocal and multiply \\(\\frac{33}{14}\\) X \\(\\frac{28}{105}\\) =<br \/>\n\\(\\frac{33 X 28}{14 X 105}\\) = \\(\\frac{462}{1470}\\), as both goes in 42,<br \/>\n42 X 11 = 462, 42 X 35 = 1470, (11, 35) = \\(\\frac{11}{35}\\).<br \/>\nTherefore 2\\(\\frac{5}{14}\\) \u00f7 (2\\(\\frac{5}{8}\\) X 1\\(\\frac{3}{7}\\)) =<br \/>\n\\(\\frac{11}{35}\\).<\/p>\n<p>Question 45.<br \/>\n<strong>LOGIC<\/strong><br \/>\nYour friend uses the model shown to state that <img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27273\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-227.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 227\" width=\"99\" height=\"39\" \/>. Is your friend correct? Justify your answer using the model.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27272\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-227.1.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 227.1\" width=\"443\" height=\"136\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-227.1.png 443w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-227.1-300x92.png 300w\" sizes=\"(max-width: 443px) 100vw, 443px\" \/><br \/>\nNo, friend is incorrect,<\/p>\n<p>Explanation :<br \/>\nGiven expression as 2\\(\\frac{1}{2}\\) \u00f7 1\\(\\frac{1}{6}\\),<br \/>\nFirst we write mixed fraction into fraction for 2\\(\\frac{1}{2}\\) as<br \/>\n(2 X 2 + 1 by 2) = \\(\\frac{5}{2}\\) and 1\\(\\frac{1}{6}\\) =<br \/>\n(1 X 6 + 1 by 6) = \\(\\frac{7}{6}\\) now we wrtie reciprocal and multiply<br \/>\n\\(\\frac{5}{2}\\) X \\(\\frac{6}{7}\\) = \\(\\frac{5 X 6}{2 X 7}\\) =<br \/>\n\\(\\frac{30}{14}\\) further we\u00a0 can simplify as both goes in 2, 2 X 15 = 30,<br \/>\n2 x 7 = 14, (15, 7), \\(\\frac{30}{14}\\) =\u00a0 \\(\\frac{15}{7}\\) as numerator<br \/>\nis greator we write as (2 X 7 + 1 by 7) = 2\\(\\frac{1}{7}\\) and<br \/>\nfriend says it is 2\\(\\frac{1}{6}\\) which is incorrect and model is showing<br \/>\n2, 1\\(\\frac{1}{6}\\) and one piece is remaining but we<br \/>\nare getting 2\\(\\frac{1}{7}\\) which is not matching, So freind is incorrect.<\/p>\n<p>Question 46.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nA bag contains 42 cups of dog food. Your dog eats 2\\(\\frac{1}{3}\\) cups of dog food each day. Is there enough food to last 3 weeks? Explain.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27298\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-228.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 228\" width=\"239\" height=\"183\" \/><br \/>\nNo, there is not enough food to last for 3 weeks,<\/p>\n<p>Explanation:<br \/>\nGiven dog eats 2\\(\\frac{1}{3}\\) cups of dog food each day,<br \/>\nnow for 3 weeks means 3 X 7 X 2\\(\\frac{1}{3}\\) , We write<br \/>\nmixed fraction 2\\(\\frac{1}{3}\\)\u00a0 as ( 2 X 3 + 1 by 3) =\\(\\frac{7}{3}\\) =<br \/>\n3 X 7 X \\(\\frac{7}{3}\\) = \\(\\frac{3 X 7 X 7}{3}\\) = \\(\\frac{147}{3}\\),<br \/>\nas both goes in 3, 3 X 49, 3 X 1 = 3,(49, 1) = \\(\\frac{147}{3}\\) = 49.<br \/>\nWe need 49 cups of dog food and bag contains 42 cups so shortage of 7 cups,<br \/>\nTherefore we do not have enough food to last for 3 weeks.<\/p>\n<p>Question 47.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nYou have 12 cups of granola and 8\\(\\frac{1}{2}\\) cups of peanuts to make trail mix. What is the greatest number of full batches of trail mix you can make? Explain how you found your answer.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27299\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-229.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 229\" width=\"287\" height=\"178\" \/><br \/>\n4 is the greatest number of full batches of trail mix I can make,<\/p>\n<p>Explanation:<br \/>\nGiven I have 12 cups of granola and 8\\(\\frac{1}{2}\\) cups of<br \/>\npeanuts to make trail mix, trail mix has 2\\(\\frac{3}{4}\\) cups of granola<br \/>\nand 1\\(\\frac{1}{3}\\) cups of peanuts,<br \/>\nFirst granola mix 12 \u00f7 2\\(\\frac{3}{4}\\), We write mixed fraction<br \/>\nas fraction as (2 X 4 + 3 by 4) = \\(\\frac{11}{4}\\) now we write reciprocal<br \/>\nand multiply as 12 X \\(\\frac{4}{11}\\) = \\(\\frac{12 X 4}{11}\\) =<br \/>\n\\(\\frac{48}{11}\\) as numerator is greater we write as<br \/>\n( 4 X 11 + 4 by 11) = 4\\(\\frac{4}{11}\\), Now peanuts mix<br \/>\n8\\(\\frac{1}{2}\\) \u00f7 1\\(\\frac{1}{3}\\),We write mixed fractions<br \/>\nas fractions as (8 X 2 + 1 by 2) = \\(\\frac{17}{2}\\) and 1\\(\\frac{1}{3}\\) =<br \/>\n(1 X 3 + 1 by 3) = \\(\\frac{4}{3}\\), Now we write reciprocal and multiply<br \/>\n\\(\\frac{17}{2}\\) X \\(\\frac{3}{4}\\) = \\(\\frac{17 X 3}{2 X 4}\\) =<br \/>\n\\(\\frac{51}{8}\\), as numerator\u00a0is greater we write as (6 X 8 + 3 by 8)=<br \/>\n6\\(\\frac{3}{8}\\). Therefore I can make 4 full batches.<\/p>\n<p>Question 48.<br \/>\n<strong>REASONING<\/strong><br \/>\nAt a track and \ufb01eld meet, the longest shot-put throw by a boy is 25 feet 8 inches. The longest shot-put throw by a girl is 19 feet 3 inches. How many times greater is the longest shot-put throw by the boy than by the girl?<\/p>\n<p>1.33 times greater is the longest shot-put throw by the boy than by the girl,<\/p>\n<p>Explanation:<br \/>\nGiven at a track and \ufb01eld meet, the longest shot-put<br \/>\nthrow by a boy is 25 feet 8 inches. The longest shot-put throw<br \/>\nby a girl is 19 feet 3 inches.<br \/>\nAs we know 1 feet is equal to 12 inches we convert first into inches as<br \/>\nBoy throw = 25 X 12 + 8 = 308 inches<br \/>\nGirl throw = 19 X 12 +\u00a0 3 = 228 + 3 = 231 inches.<br \/>\nNow\u00a0 boy record to girl record is \\(\\frac{308}{231}\\) = 1.3333,<br \/>\nTherefore 1.33 times greater is the longest shot-put throw by<br \/>\nthe boy than by the girl.<\/p>\n<h3><a id=\"Lesson_2.4_Adding_and_Subtracting_Decimals\"><\/a>Lesson 2.4 Adding and Subtracting Decimals<\/h3>\n<p><strong>EXPLORATION 1<\/strong><br \/>\n<strong>Using Number Lines<\/strong><br \/>\n<strong>Work with a partner. Use each number line to \ufb01nd A + B and B &#8211; A. Explain how you know you are correct.<\/strong><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27274\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-230.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 230\" width=\"550\" height=\"163\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-230.png 550w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-230-300x89.png 300w\" sizes=\"(max-width: 550px) 100vw, 550px\" \/><br \/>\na. A + B = 1.1 and\u00a0 B &#8211; A = 0.5<br \/>\nb. A + B = 2.24 and B &#8211; A = 0.02<br \/>\nc. A + B = 7.6 and B &#8211; A = 0.8<br \/>\nd. A + B = 5.1 and B &#8211; A = 0.8<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-51179\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-50.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-50\" width=\"1294\" height=\"449\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-50.bmp 1294w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-50-300x104.jpg 300w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-50-1024x355.jpg 1024w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-50-768x266.jpg 768w\" sizes=\"(max-width: 1294px) 100vw, 1294px\" \/><br \/>\na. A + B = 1.1 and\u00a0 B- A = 0.5<br \/>\nExplanation:<br \/>\na. Given A is at 0.3 and B is at 0.8,<br \/>\nnow A + B = 0.3 + 0.8 = 1.1,<br \/>\nB &#8211; A = 0.8 &#8211; 0.3 = 0.5<\/p>\n<p>b. Given A is at 1.11and B is at 1.13,<br \/>\nA + B = 1.11 + 1.13 = 2.24<br \/>\nB &#8211; A = 1.13 &#8211; 1.11 = 0.02<\/p>\n<p>c. Given A is at 3.4 and b is at 4.2<br \/>\nA + B = 3.4\u00a0 + 4.2 = 7.6<br \/>\nA &#8211; B = 4.2 &#8211; 3.4 = 0.8<\/p>\n<p>d. Given A is at 2.15 and b is at 2.95<br \/>\nA + B = 2.15 + 2.95 = 5.1<br \/>\nA &#8211; B = 2.95 &#8211; 2.15 = 0.8<\/p>\n<p>Explained in the picture above.<\/p>\n<p><strong>EXPLORATION 2<\/strong><br \/>\n<strong>Work with a partner. Explain how you can use the place value chart below to add and subtract decimals beyond hundredths. Then \ufb01nd each sum or difference.<\/strong><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27275\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-231.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 231\" width=\"568\" height=\"272\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-231.png 568w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-231-300x144.png 300w\" sizes=\"(max-width: 568px) 100vw, 568px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27302\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-232.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 232\" width=\"155\" height=\"215\" \/><br \/>\na. 16.05 + 2.945<br \/>\nb. 7.421 + 8.058<br \/>\nc. 38.72 &#8211; 8.618<br \/>\nd. 64.968 &#8211; 51.167<br \/>\ne. 225.1 + 85.0465<br \/>\nf. 1107.20592 &#8211; 102.3056<br \/>\na. 16.05 + 2.945 = 18.995<br \/>\nb. 7.421 + 8.058 = 15.479<br \/>\nc. 38.72 &#8211; 8.618 = 30.102<br \/>\nd. 64.968 &#8211; 51.167 = 13.801<br \/>\ne. 225.1 + 85.0465 = 310.1465<br \/>\nf. 1107.20592 &#8211; 102.3056 = 1004.90032<br \/>\nExplanation:<br \/>\na. 16.05 + 2.945 = 18.995<br \/>\nHere we have thousandths value as 0.000 + 0.005 =0.005<br \/>\nand wrote as below shown at thousandths place,<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-51208\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-51-3.bmp\" alt=\"Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-51\" width=\"734\" height=\"272\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-51-3.bmp 734w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-51-3-300x111.jpg 300w\" sizes=\"(max-width: 734px) 100vw, 734px\" \/><\/p>\n<p>b. 7.421 + 8.058 = 15.479<br \/>\nHere we have thousandths value as 0.001 + 0.0008 = 0.0009 and<br \/>\nwrote as below shown at thousandths place, 0.0009,<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-51207\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-52-2.bmp\" alt=\"Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-52\" width=\"729\" height=\"272\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-52-2.bmp 729w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-52-2-300x112.jpg 300w\" sizes=\"(max-width: 729px) 100vw, 729px\" \/><br \/>\nc. 38.72 &#8211; 8.618 = 30.102<br \/>\nHere we have thousandths s value as 0.000 here we take 1<br \/>\nfrom tenths place and we get 10 at thousandths place and<br \/>\nsubtract 0.008 we get 0.002 at thousandths place<br \/>\nand wrote as below shown at thousandths place,<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-51209\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-53-1.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-53\" width=\"690\" height=\"296\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-53-1.bmp 690w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-53-1-300x129.jpg 300w\" sizes=\"(max-width: 690px) 100vw, 690px\" \/><\/p>\n<p>d. 64.968 &#8211; 51.167 = 13.801<br \/>\nHere we have thousandths s value as 0.008 and<br \/>\nsubtract 0.007 we get 0.001 at thousandths place<br \/>\nand wrote as below shown at thousandths place,<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-51197\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-54.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-54\" width=\"690\" height=\"296\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-54.bmp 690w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-54-300x129.jpg 300w\" sizes=\"(max-width: 690px) 100vw, 690px\" \/>e. 225.1 + 85.0465 = 310.1465<br \/>\nHere we have thousandths value as 0.000 + 0.005 =0.005<br \/>\nand wrote as below shown at thousandths place,<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-51210\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-55.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-55\" width=\"690\" height=\"270\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-55.bmp 690w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-55-300x117.jpg 300w\" sizes=\"(max-width: 690px) 100vw, 690px\" \/><br \/>\nf. 1107.20592 &#8211; 102.3056 = 1004.90032<br \/>\nHere we have ten thousandths value as 0.0002 &#8211; 0.0000 =0.00002<br \/>\nand thousandths values as 0.0009 &#8211; 0.0006 = 0.0003,<br \/>\nwrote as below shown at thousandths places,<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-51213\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-56.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-56\" width=\"690\" height=\"272\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-56.bmp 690w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-56-300x118.jpg 300w\" sizes=\"(max-width: 690px) 100vw, 690px\" \/><\/p>\n<p><strong>2.4 Lesson<\/strong><\/p>\n<p><strong>Key Idea<\/strong><br \/>\nAdding and Subtracting Decimals<br \/>\nTo add or subtract decimals, write the numbers vertically and line up the decimal points. Then bring down the decimal point and add or subtract as you would with whole numbers.<\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Add.<\/strong><\/p>\n<p>Question 1.<br \/>\n4.206 + 10.85<br \/>\n4.206<br \/>\n(+) 10.850\u00a0<span style=\"text-decoration: underline;\"><br \/>\n1<br \/>\n15.056\u00a0 \u00a0 \u00a0<\/span><br \/>\nExplanation:<br \/>\n4.206<br \/>\n(+) 10.850\u00a0<span style=\"text-decoration: underline;\"><br \/>\n1<br \/>\n15.056\u00a0 \u00a0 \u00a0<\/span><br \/>\nhere we add according to their unit place values respectively.<\/p>\n<p>Question 2.<br \/>\n15.5 + 8.229<br \/>\n15.500<br \/>\n(+)\u00a0 8.229<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a01<br \/>\n<\/span><span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a023.729\u00a0 \u00a0<\/span><br \/>\nExplanation:<br \/>\n15.500<br \/>\n(+)\u00a0 8.229<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a01\u00a0 \u00a0 \u00a0 \u00a0\u00a0<\/span><\/p>\n<p><span style=\"text-decoration: underline;\"><br \/>\n<\/span><span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a023.729\u00a0 \u00a0<\/span><br \/>\nhere we add according to their unit place values respectively.<\/p>\n<p>Question 3.<br \/>\n78.41 + 90.99<br \/>\n78.41<br \/>\n(+)90.99<span style=\"text-decoration: underline;\"><br \/>\n1\u00a0 \u00a011<br \/>\n169.40<br \/>\n<\/span>Explanation:<br \/>\n78.41<br \/>\n(+)90.99<span style=\"text-decoration: underline;\"><br \/>\n1\u00a0 \u00a011<br \/>\n169.40\u00a0 \u00a0<\/span><br \/>\nhere we add according to their unit place values respectively.<\/p>\n<p><strong>Subtract<\/strong><\/p>\n<p>Question 4.<br \/>\n6.34 &#8211; 5.33<br \/>\n6.34<br \/>\n<span style=\"text-decoration: underline;\">(-)5.33<br \/>\n1.01\u00a0 \u00a0 \u00a0<\/span><\/p>\n<p>Explanation:<br \/>\n6.34<br \/>\n<span style=\"text-decoration: underline;\">(-)5.33<br \/>\n1.01\u00a0 \u00a0\u00a0<\/span><span style=\"text-decoration: underline;\"><br \/>\n<\/span>here we subtract according to their unit place values respectively.<span style=\"text-decoration: underline;\"><br \/>\n<\/span><\/p>\n<p>Question 5.<br \/>\n27.9 &#8211; 0.905<br \/>\n6,18,9,10<br \/>\n27.900<br \/>\n<span style=\"text-decoration: underline;\">(-)\u00a0 0.905<br \/>\n26.995<br \/>\n<\/span>Explanation:<span style=\"text-decoration: underline;\"><br \/>\n<\/span>\u00a0 6,18,9,10<span style=\"text-decoration: underline;\"><br \/>\n27.900<br \/>\n(-)\u00a0 0.905<br \/>\n26.995<br \/>\n<\/span>here we subtract according to their unit place values respectively.<span style=\"text-decoration: underline;\"><br \/>\n<\/span><\/p>\n<p>Question 6.<br \/>\n18.626 &#8211; 13.88<br \/>\n7,15,12<br \/>\n18.626<br \/>\n<span style=\"text-decoration: underline;\">(-)13.880<br \/>\n4.746<br \/>\n<\/span>Explanation:<br \/>\n7,15,12<br \/>\n18.626<br \/>\n<span style=\"text-decoration: underline;\">(-)13.880<br \/>\n4.746<br \/>\n<\/span>here we subtract according to their unit place values respectively.<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-51216\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-57.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-57\" width=\"802\" height=\"388\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-57.bmp 802w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-57-300x145.jpg 300w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-57-768x372.jpg 768w\" sizes=\"(max-width: 802px) 100vw, 802px\" \/><br \/>\n<strong>Try It<br \/>\n<\/strong>Question 7.<br \/>\n<strong>WHAT IF?<\/strong><br \/>\nThe execution score is adjusted and has 1.467 in deductions. What is the gymnast\u2019s score?<\/p>\n<p>The gymnast&#8217;s score is 15.133<\/p>\n<p>Explanation:<br \/>\nEvaluating the expression to solve the problem,<br \/>\n= 6.9 + (10 &#8211; 1.467) -0.3,<br \/>\n= 6.9 + (8.533) &#8211; 0.3<br \/>\n= 15.433 &#8211; 0.3 = 15.133,<br \/>\ntherefore the gymnast&#8217;s score is 15.133.<\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><br \/>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p><strong>ADDING AND SUBTRACTING DECIMALS<\/strong><br \/>\n<strong>Evaluate the expression.<\/strong><\/p>\n<p>Question 8.<br \/>\n23.557 &#8211; 17.601 + 5.216<\/p>\n<p>23.557 &#8211; 17.601 + 5.216 = 11.172<br \/>\nExplanation:<br \/>\n1,12,15<br \/>\n2 3 . 5 5\u00a0 7<br \/>\n<span style=\"text-decoration: underline;\">(-) 1 7.\u00a0 6 0\u00a0 1<br \/>\n5.\u00a0 \u00a09\u00a0 5\u00a0 6<br \/>\n<\/span>Now add 5.956 with 5.216<br \/>\n5.956<br \/>\n(+)\u00a0 5.216\u00a0<span style=\"text-decoration: underline;\"><br \/>\n1\u00a0 \u00a0 1<br \/>\n11.172<br \/>\n<\/span>Therefore we get 23.557 &#8211; 17.601 + 5.216 = 11.172.<\/p>\n<p>Question 9.<br \/>\n16.5263 + 12.404 &#8211; 11.73<\/p>\n<p>16.5263 + 12.404 &#8211; 11.73 = 17.2003<br \/>\nExplanation:<br \/>\n16.5263<br \/>\n(+)12.4040<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a01\u00a0 \u00a0 \u00a0\u00a0<\/span><br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a028.9303<br \/>\n<\/span>Now we subtract 11.73 from 28.9303<br \/>\n28.9303<br \/>\n<span style=\"text-decoration: underline;\">(-)11.7300\u00a0<\/span><br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 17.2003<br \/>\n<\/span>Therefore we get 16.5263 + 12.404 &#8211; 11.73 = 17.2003.<\/p>\n<p>Question 10.<br \/>\n<strong>CHOOSE TOOLS<\/strong><br \/>\nWhy is it helpful to estimate the answer before adding or subtracting decimals?<\/p>\n<p>Estimation is useful when we don\u2019t need an exact answer.<br \/>\nIt also lets you check to be sure an exact answer is close<br \/>\nto being correct. Estimating with decimals works<br \/>\njust the same as estimating with whole numbers.<br \/>\nWhen rounding the values to be added, subtracted,<br \/>\nmultiplied, or divided, it helps to round to numbers<br \/>\nthat are easy to work with.<\/p>\n<p>Question 11.<br \/>\n<strong>WRITING<\/strong><br \/>\nWhen adding or subtracting decimals, how can you be sure to add or subtract only digits that have the same place value?<br \/>\nWhen adding and subtracting decimals we use few steps as below:<b><br \/>\n<\/b>1) We line up the place values of the numbers by lining up the decimals.<br \/>\n2) We Add in filler zeros if needed.<br \/>\n3) Adding or Subtracting the numbers in the same place value positions.<br \/>\nExamples<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-51221\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-58.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-58\" width=\"679\" height=\"368\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-58.bmp 679w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-58-300x163.jpg 300w\" sizes=\"(max-width: 679px) 100vw, 679px\" \/><\/p>\n<p>Question 12.<br \/>\n<strong>OPEN-ENDED<\/strong><br \/>\nDescribe two real-life examples of when you would need to add and subtract decimals.<\/p>\n<p>We deal with decimal addition and subtraction in everyday<br \/>\nlife while dealing with:<br \/>\n<span style=\"font-size: 16px;\">Money<br \/>\n<\/span><span style=\"font-size: 16px;\">Measurements (Length, Mass, Capacity)<br \/>\n<\/span><span style=\"font-size: 16px;\">Temperature<\/span><span style=\"font-size: 16px;\"><br \/>\n<\/span><\/p>\n<p>Decimals can be added or subtracted in the same way as we add or subtract whole numbers.<\/p>\n<p>Example:<br \/>\na. Kate had $ 368.29. Her mother gave her $ 253.46 and her<br \/>\nsister gave her $ 57.39. How much money does she has now?<br \/>\nAnswer:<br \/>\nMoney Kate had \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 =\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 $ 368.29<br \/>\nMoney gave her mother\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0=\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 $ 253.46<br \/>\nMoney gave her sister\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 =\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <u>+\u00a0\u00a0 $\u00a0\u00a0 57.39<br \/>\n<\/u>Total money she has now\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0= \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 $ 679.14<\/p>\n<p>b. Kylie had 25 m of ribbon. She uses 8 m and 13 cm to<br \/>\ndecorate a skirt. How much ribbon is remaining with Kylie?<br \/>\nAnswer:<br \/>\nLength of ribbon Kylie had = 25 m = 25.00<br \/>\nLength of ribbon used by Kylie = 8 m 13 cm = 8.13<br \/>\nThe remaining length of ribbon = 25.00 \u2013 8.13\u00a0= 16.87<\/p>\n<div><img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-51255\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-60.bmp\" alt=\"Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-60\" width=\"396\" height=\"101\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-60.bmp 396w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-60-300x77.jpg 300w\" sizes=\"(max-width: 396px) 100vw, 396px\" \/><\/div>\n<p>Question 13.<br \/>\n<strong>STRUCTURE<\/strong><br \/>\nYou add 3.841 + 29.999 as shown. Describe a method for adding the numbers using mental math. Which method do you prefer? Explain.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27300\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-232.1.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 232.1\" width=\"91\" height=\"84\" \/><br \/>\nI prefer the way as we add or subtract whole numbers as shown above<br \/>\nthan the mental math method.<\/p>\n<p>Explanation:<br \/>\nRounding is a mental math strategy for adding and subtracting numbers.<br \/>\nWhen you round, you will likely need to adjust your answer to get<br \/>\nthe exact answer.<br \/>\nFor Example:<br \/>\n23 + 58 can be rounded to 20 + 60 = 80.<br \/>\n23 is 3 more than 20 and 58 is 2 less than 60.(3 -2)<br \/>\nSo adjust answer by adding 1. (80 + 1), Answer is 81.<br \/>\nExample:<br \/>\n76 &#8211; 40 can be rounded to 80 &#8211; 40 = 40.<br \/>\n76 is 4 less than 80. So adjust answer by subtracting 4.<br \/>\n(40- 4) , Answer is 36.<\/p>\n<p>Question 14.<br \/>\n<strong>OPEN-ENDED<\/strong><br \/>\nWrite three decimals that have a sum of 27.905.<br \/>\nThe three decimals are 15.812, 4.670, 7.423 to have a sum of 27.905<\/p>\n<p>Explanation:<br \/>\nWe take any decimals randomly as 15.812, 4.670, 7.423,<br \/>\nwe have sum of 27.905 as<br \/>\n15.812<br \/>\n4.670<br \/>\n(+)7.423<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 11\u00a0 1<br \/>\n27.905<br \/>\n<\/span>Therefore, the three decimals are 15.812, 4.670, 7.423<br \/>\nto have a sum of 27.905.<\/p>\n<p><strong>Self-Assessment for Problem Solving<\/strong><br \/>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 15.<br \/>\nA \ufb01eld hockey \ufb01eld is rectangular. Its width is 54.88 meters, and its perimeter is 289.76 meters. Find the length of the \ufb01eld.<br \/>\nThe length of hockey field is 90 meters<\/p>\n<p>Explanation:<br \/>\nGiven a \ufb01eld hockey \ufb01eld is rectangular. Its width is 54.88 meters<br \/>\nand its perimeter is 289.76 meters.<br \/>\nWe know perimeter of rectangle is 2( length + width),<br \/>\nSo, 289.76 = 2(length + 54.88)<br \/>\nlength + 54.88 = \\(\\frac{289.76}{2}\\),<br \/>\nlength + 54.88 = 144.88,<br \/>\nlength = 144.88 &#8211; 54.88 = 90 meters,<br \/>\nTherefore the length of hockey field is 90 meters.<\/p>\n<p>Question 16.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nYou mix 23.385 grams of sugar and 12.873 grams of baking soda<br \/>\nin a glass container for an experiment. You place the container on a<br \/>\nscale to \ufb01nd that the total mass is 104.2 grams.<br \/>\nWhat is the mass of the container?<\/p>\n<p>The mass of the container is 67.942 grams<\/p>\n<p>Explanation:<br \/>\nGiven I\u00a0mix 23.385 grams of sugar and 12.873 grams of baking soda<br \/>\nin a glass container for an experiment. You place the container on a<br \/>\nscale to \ufb01nd that the total mass is 104.2 grams. So the mass of the container<br \/>\nis 104.2 &#8211; (23.385 + 12.873) =104.2 &#8211; 36.258 = 67.942 grams.<br \/>\nTherefore the mass of the container is 67.942 grams.<\/p>\n<p>Question 17.<br \/>\nOne molecule of water is made of two hydrogen atoms and one oxygen atom. The masses (in atomic mass units) for one atom of hydrogen and oxygen are shown. What is the mass (in atomic mass units) of one molecule of water?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27301\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-232.2.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 232.2\" width=\"132\" height=\"240\" \/><br \/>\nThe mass of one molecule of water is 18.0148 amu<br \/>\n(amu = atomic mass units)<\/p>\n<p>Explanation:<br \/>\nGiven One molecule of water is made of two hydrogen<br \/>\natomsand one oxygen atom. The mass of one atom of<br \/>\nhydrogen is 1.0079 amu and oxygen is 15.999 amu.<br \/>\nSo the mass of one molecule of water is (2 X 1.0079) + 15.999,<br \/>\n= 2.0158 + 15.999 = 18.0148 amu, therefore the mass of<br \/>\none molecule of water is 18.0148 amu.<\/p>\n<h3><a id=\"Adding_and_Subtracting_Decimals_Homework_&amp;_Practice_2.4\"><\/a>Adding and Subtracting Decimals Homework &amp; Practice 2.4<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p>Divide. Write the answer in simplest form.<\/p>\n<p>Question 1.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27303\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-233.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 233\" width=\"62\" height=\"49\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27303\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-233.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 233\" width=\"62\" height=\"49\" \/>= \\(\\frac{13}{3}\\) = 4\\(\\frac{1}{3}\\)<br \/>\nExplanation:<br \/>\nGiven expressions as 3\\(\\frac{1}{4}\\) \u00f7 \\(\\frac{3}{4}\\),<br \/>\nFirst we write mixed fraction into fraction 3\\(\\frac{1}{4}\\) as<br \/>\n(3 X 4 + 1 by 4) = \\(\\frac{13}{4}\\),Now \\(\\frac{3}{4}\\) we<br \/>\nwrite as reciprocal and multiply \\(\\frac{4}{3}\\) as<br \/>\n\\(\\frac{13}{4}\\) X \\(\\frac{4}{3}\\) = \\(\\frac{13 X 4}{4 X 3}\\) =<br \/>\n\\(\\frac{52}{12}\\) as both goes in 4, 4 X 13 = 52,<br \/>\n4 X 3 = 12, (13, 3) = \\(\\frac{13}{3}\\) as numerator is greater<br \/>\nwe write as (4 X 3 + 1 by 3)= 4\\(\\frac{1}{3}\\).<br \/>\nTherefore 3\\(\\frac{1}{4}\\) \u00f7 \\(\\frac{3}{4}\\) = \\(\\frac{13}{3}\\) = 4\\(\\frac{1}{3}\\).<\/p>\n<p>Question 2.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27304\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-234.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 234\" width=\"65\" height=\"48\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27304\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-234.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 234\" width=\"65\" height=\"48\" \/>= \\(\\frac{5}{6}\\)<br \/>\nExplanation:<br \/>\nGiven expressions as 4\\(\\frac{1}{6}\\) \u00f7 5<br \/>\nFirst we write mixed fraction into fraction 4\\(\\frac{1}{6}\\) as<br \/>\n(4 X 6 + 1 by 6) = \\(\\frac{25}{6}\\), Now 5 we<br \/>\nwrite as reciprocal and multiply \\(\\frac{1}{5}\\) as<br \/>\n\\(\\frac{25}{6}\\) X \\(\\frac{1}{5}\\) = \\(\\frac{25 X 1}{6 X 5}\\) =<br \/>\n\\(\\frac{25}{30}\\) as both goes in 5, 5 X 5 = 25,<br \/>\n5 X 6 = 30, (5, 6) = \\(\\frac{5}{6}\\),<br \/>\nTherefore 4\\(\\frac{1}{6}\\) \u00f7 5 = \\(\\frac{5}{6}\\).<\/p>\n<p>Question 3.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27305\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-235.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 235\" width=\"77\" height=\"52\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27305\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-235.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 235\" width=\"77\" height=\"52\" \/>= \\(\\frac{25}{12}\\) = 2\\(\\frac{1}{12}\\)<br \/>\nExplanation:<br \/>\nGiven expressions as 6\\(\\frac{2}{3}\\) \u00f7 3\\(\\frac{1}{5}\\),<br \/>\nFirst we write mixed fractions into fractions 6\\(\\frac{2}{3}\\) as<br \/>\n(6 X 3 + 2 by 3) = \\(\\frac{20}{3}\\) and 3\\(\\frac{1}{5}\\) as<br \/>\n(3 X 5 + 1 by 5) = \\(\\frac{16}{5}\\),Now \\(\\frac{16}{5}\\) we<br \/>\nwrite as reciprocal and multiply \\(\\frac{5}{16}\\) as<br \/>\n\\(\\frac{20}{3}\\) X \\(\\frac{5}{16}\\) = \\(\\frac{20 X 5}{3 X 16}\\) =<br \/>\n\\(\\frac{100}{48}\\) as both goes in 4, 4 X 25 = 100,<br \/>\n4 X 12 = 48, (25, 12) = \\(\\frac{25}{12}\\) as numerator is greater<br \/>\nwe write as (2 X 12 + 1 by 12)= 2\\(\\frac{1}{12}\\).<br \/>\nTherefore 6\\(\\frac{2}{3}\\) \u00f7 3\\(\\frac{1}{5}\\) = \\(\\frac{25}{12}\\) = 2\\(\\frac{1}{12}\\).<\/p>\n<p><strong>Find the GCF of the numbers.<\/strong><\/p>\n<p>Question 4.<br \/>\n16, 28, 40<\/p>\n<p>The GCF of 16, 28, 40 is 4<\/p>\n<p>Explanation:<br \/>\nFactors of 16 are 1, 2, 4, 8, 16<br \/>\nFactors of 28 are 1, 2, 4, 7, 14, 28<br \/>\nFactors of 40 are 1, 2, 4, 5, 8, 10, 20, 40<br \/>\nas 4 is the greatest common number in all the three,<br \/>\ntherefore GCF (16, 28, 40) is 4.<\/p>\n<p>Question 5.<br \/>\n39, 54, 63<\/p>\n<p>The GCF of 39, 54, 63 is 3<\/p>\n<p>Explanation:<br \/>\nFactors of 39 are 1, 3, 13 and 39<br \/>\nFactors of 54 are 1, 2, 3, 6, 9, 18, 27 and 54<br \/>\nFactors of 63 are 1, 3, 7, 9, 21 and 63<br \/>\nas 3 is the greatest common number in the three,<br \/>\ntherefore GCF (39, 54, 63) is 3.<\/p>\n<p>Question 6.<br \/>\n24, 72, 132<\/p>\n<p>The GCF of 24, 72, 132 is<\/p>\n<p>Explanation:<br \/>\nFactors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24<br \/>\nFactors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and 72<br \/>\nFactors of 132 are 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66 and 132<br \/>\nas 12 is the greatest common number in all the three,<br \/>\ntherefore GCF (24, 72, 132) is 12.<\/p>\n<p><strong>Find the value of the power.<\/strong><\/p>\n<p>Question 7.<br \/>\n1<sup>12<\/sup><\/p>\n<p>1<sup>12 <\/sup>= 1<\/p>\n<p>Explanation:<br \/>\n1 to the power of 12 means we multiply 1 by<br \/>\n12 times as 1 X 1 X 1 X 1 X 1 X 1 X 1 X 1 X 1 X 1 X 1 X 1 = 1.<\/p>\n<p>Question 8.<br \/>\n2<sup>4<\/sup><\/p>\n<p>2<sup>4 <\/sup>= 16<\/p>\n<p>Explanation:<br \/>\n2 to the power of 4 means we multiply 2 by<br \/>\n4 times as 2 X 2 X 2 X 2 = 16.<\/p>\n<p>Question 9.<br \/>\n3<sup>6<\/sup><\/p>\n<p>3<sup>6 <\/sup>= 729<\/p>\n<p>Explanation:<br \/>\n3 to the power of 6 means we multiply 3 by<br \/>\n6 times as 3 X 3 X 3 X 3 X 3 X 3 = 729.<\/p>\n<p>Question 10.<br \/>\n5<sup>4<br \/>\n<\/sup>5<sup>4 <\/sup>= 625<\/p>\n<p>Explanation:<br \/>\n5 to the power of 4 means we multiply 5 by<br \/>\n4 times as 5 X 5 X 5 X 5 = 625.<br \/>\n<strong><br \/>\nClassify the quadrilateral.<\/strong><\/p>\n<p>Question 11.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27306\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-236.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 236\" width=\"143\" height=\"135\" \/><br \/>\nSquare<\/p>\n<p>Explanation:<br \/>\nQuadrilaterals can be classified into Parallelograms,<br \/>\nSquares, Rectangles , Trapezoids and Rhombuses.<br \/>\nAs given in the picture above it is a square because,<br \/>\nAll sides are equal,<br \/>\nEach angle is a right angle,<br \/>\nOpposite sides are equal.<br \/>\nSo, it is a square.<\/p>\n<p>Question 12.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27307\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-237.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 237\" width=\"147\" height=\"146\" \/><br \/>\nTrapezoid<\/p>\n<p>Explanation:<br \/>\nQuadrilaterals can be classified into Parallelograms,<br \/>\nSquares, Rectangles , Trapezoids and Rhombuses.<br \/>\nAs given in the picture above it is a trapezoid because,<br \/>\nOpposite sides are parallel.<br \/>\nAdjacent angles add up to 180\u00b0.<br \/>\nSo, it is a Trapezoid.<\/p>\n<p>Question 13.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27308\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-238.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 238\" width=\"140\" height=\"152\" \/><br \/>\nParallelogram<\/p>\n<p>Explanation:<br \/>\nQuadrilaterals can be classified into Parallelograms,<br \/>\nSquares, Rectangles , Trapezoids and Rhombuses.<br \/>\nAs given in the picture above it is a parrelogram because,<br \/>\nOpposite sides are parallel.<br \/>\nOpposites sides are equal.<br \/>\nOpposite angles are equal.<br \/>\nAll sides are equal,<br \/>\nSo it is a parallelogram.<\/p>\n<p><strong>Concepts, Skills, &amp; Problem Solving<\/strong><br \/>\n<strong>USING TOOLS<\/strong><br \/>\n<strong>Use a place value chart to \ufb01nd the sum or difference.<\/strong> (See Exploration 2, p. 67.)<\/p>\n<p>Question 14.<br \/>\n4.63 + 8.547<br \/>\n4.63 + 8.547 = 13.177<\/p>\n<p>Explanation:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-51507\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-61.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-61\" width=\"690\" height=\"270\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-61.bmp 690w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-61-300x117.jpg 300w\" sizes=\"(max-width: 690px) 100vw, 690px\" \/><\/p>\n<p>Question 15.<br \/>\n3.6257 &#8211; 2.98 = 0.6457<\/p>\n<p>Explanation:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-51508\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-62.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-62\" width=\"690\" height=\"270\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-62.bmp 690w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-62-300x117.jpg 300w\" sizes=\"(max-width: 690px) 100vw, 690px\" \/><\/p>\n<p>Question 16.<br \/>\n14.065 + 13.8542 = 27.9192<\/p>\n<p>Explanation:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-51509\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-63-1.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-63\" width=\"690\" height=\"270\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-63-1.bmp 690w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-63-1-300x117.jpg 300w\" sizes=\"(max-width: 690px) 100vw, 690px\" \/><\/p>\n<p><strong>ADDING DECIMALS<\/strong><br \/>\n<strong>Add.<\/strong><\/p>\n<p>Question 17.<br \/>\n7.82 + 3.209<br \/>\n7.82 + 3.209 = 11.029<\/p>\n<p>Explanation:<br \/>\n<span style=\"text-decoration: underline;\">1,1<\/span><br \/>\n7.820<br \/>\n<span style=\"text-decoration: underline;\">(+)3.209<br \/>\n11.029<br \/>\n<\/span>We added digits according to their place values.<\/p>\n<p>Question 18.<br \/>\n3.7 + 2.77<br \/>\n3.7 + 2.77 = 6.47<\/p>\n<p>Explanation<br \/>\n<span style=\"text-decoration: underline;\">1,<\/span><br \/>\n3.70<br \/>\n<span style=\"text-decoration: underline;\">(+)2.77<br \/>\n6.47<br \/>\n<\/span>We added digits according to their place values.<\/p>\n<p>Question 19.<br \/>\n12.829 + 10.07<br \/>\n12.829 + 10.07 = 22.899<\/p>\n<p>Explanation:<br \/>\n12.829<br \/>\n<span style=\"text-decoration: underline;\">(+)10.070<br \/>\n22.899<br \/>\n<\/span>We added digits according to their place values.<\/p>\n<p>Question 20.<br \/>\n20.35 + 13.748<br \/>\n20.35 + 13.748 = 34.098<\/p>\n<p>Explanation:<br \/>\n<span style=\"text-decoration: underline;\">1<\/span><br \/>\n20.350<br \/>\n<span style=\"text-decoration: underline;\">(+)13.748<br \/>\n34.098<br \/>\n<\/span>We added digits according to their place unit values.<\/p>\n<p>Question 21.<br \/>\n11.212 + 7.36<br \/>\n11.212 + 7.36 = 18.572<\/p>\n<p>Explanation:<br \/>\n11.212<br \/>\n<span style=\"text-decoration: underline;\">(+)07.360<br \/>\n18<\/span><span style=\"text-decoration: underline;\">.572<br \/>\n<\/span>We added digits according to their place unit values.<\/p>\n<p>Question 22.<br \/>\n14.91 + 2.095<br \/>\n14.91 + 2.095 = 17.005<\/p>\n<p>Explanation:<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 1,1<\/span><br \/>\n14.910<br \/>\n<span style=\"text-decoration: underline;\">(+)02.095<br \/>\n17.005<br \/>\n<\/span>We added digits according to their place unit values.\u00a0<span style=\"text-decoration: underline;\"><br \/>\n<\/span><\/p>\n<p>Question 23.<br \/>\n31.994 + 8.006<br \/>\n31.994 + 8.006 = 40<\/p>\n<p>Explanation:<br \/>\n<span style=\"text-decoration: underline;\">1,1,1,1<\/span><br \/>\n31.994<br \/>\n<span style=\"text-decoration: underline;\">(+)08.006<br \/>\n40.000<br \/>\n<\/span>We added digits according to their place unit values.<\/p>\n<p>Question 24.<br \/>\n3.946 + 6.052<br \/>\n3.946 + 6.052 = 9.998<\/p>\n<p>Explanation:<br \/>\n3.946<br \/>\n<span style=\"text-decoration: underline;\">(+)6.052<br \/>\n9.998<br \/>\n<\/span>We added digits according to their place unit values.<\/p>\n<p>Question 25.<br \/>\n41.226 + 102.774<br \/>\n41.226 + 102.774 = 144<\/p>\n<p>Explanation:<br \/>\n<span style=\"text-decoration: underline;\">1,1,1,1<\/span><br \/>\n41.226<br \/>\n<span style=\"text-decoration: underline;\">(+)102.774<br \/>\n144.000<br \/>\n<\/span>We added digits according to their place unit values.<\/p>\n<p>Question 26.<br \/>\n122.781 + 19.228<br \/>\n122.781 + 19.228 = 142.009<\/p>\n<p>Explanation:<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a01,1,1,<\/span><br \/>\n122.781<br \/>\n<span style=\"text-decoration: underline;\">(+)\u00a0 \u00a019.228<br \/>\n142.009<br \/>\n<\/span>We added digits according to their place unit values.<\/p>\n<p>Question 27.<br \/>\n17.440 + 12.497<br \/>\n17.440 + 12.497 = 29.937<\/p>\n<p>Explanation:<br \/>\n<span style=\"text-decoration: underline;\">1,<\/span><br \/>\n17.440<br \/>\n<span style=\"text-decoration: underline;\">(+)12.497<br \/>\n29.937<br \/>\n<\/span>We added digits according to their place unit values.<\/p>\n<p>Question 28.<br \/>\n15.255 + 19.058<br \/>\n15.255 + 19.058 = 34.313<\/p>\n<p>Explanation:<br \/>\n<span style=\"text-decoration: underline;\">1,\u00a0 1,1<\/span><br \/>\n15.255<br \/>\n<span style=\"text-decoration: underline;\">(+)19.058<br \/>\n34.313<br \/>\n<\/span>We added digits according to their place unit values.<\/p>\n<p><strong>SUBTRACTING DECIMALS<\/strong><br \/>\n<strong>Subtract.<\/strong><\/p>\n<p>Question 29.<br \/>\n4.58 &#8211; 3.12<br \/>\n4.58 &#8211; 3.12 = 1.46<\/p>\n<p>Explanation:<br \/>\n4.58<span style=\"text-decoration: underline;\"><br \/>\n(-)3.12<br \/>\n1.46<br \/>\n<\/span>We subtract each digit according to their place unit values.<\/p>\n<p>Question 30.<br \/>\n8.629 &#8211; 5.309<br \/>\n8.629 &#8211; 5.309 = 3.320<\/p>\n<p>Explanation:<br \/>\n8.629<span style=\"text-decoration: underline;\"><br \/>\n(-)5.309<br \/>\n3.320<br \/>\n<\/span>We subtract each digit according to their place unit values.<\/p>\n<p>Question 31.<br \/>\n6.98 &#8211; 2.614<br \/>\n6.98 &#8211; 2.614 = 4.366<\/p>\n<p>Explanation:<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 7,10\u00a0 \u00a0\u00a0<\/span><br \/>\n6.980<span style=\"text-decoration: underline;\"><br \/>\n(-) 2.614<br \/>\n4.366<br \/>\n<\/span>We subtract each digit according to their place unit values.<\/p>\n<p>Question 32.<br \/>\n15.131 &#8211; 11.57<br \/>\n15.131 &#8211; 11.57 = 3.561<\/p>\n<p>Explanation:<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a010,13\u00a0\u00a0<\/span><br \/>\n15.1\u00a0 \u00a03\u00a0 \u00a01<span style=\"text-decoration: underline;\"><br \/>\n(-)11.5\u00a0 \u00a07\u00a0 \u00a00<br \/>\n3.5\u00a0 \u00a06\u00a0 \u00a01<br \/>\n<\/span>We subtract each digit according to their place unit values.<\/p>\n<p>Question 33.<br \/>\n13.5 &#8211; 10.856<br \/>\n13.5 &#8211; 10.856 = 2.644<\/p>\n<p>Explanation:<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a015,9,10<\/span><br \/>\n13.5 0 0<span style=\"text-decoration: underline;\"><br \/>\n(-)10.8 5 6<br \/>\n2.6\u00a0 4 4<br \/>\n<\/span>We subtract each digit according to their place unit values.<\/p>\n<p>Question 34.<br \/>\n25.82 &#8211; 22.936 = 2.884<\/p>\n<p>Explanation:<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 4,17,11,10<\/span><br \/>\n25.820<span style=\"text-decoration: underline;\"><br \/>\n(-)22.936<br \/>\n2.884<br \/>\n<\/span>We subtract each digit according to their place unit values.<\/p>\n<p>Question 35.<br \/>\n17.651 &#8211; 12.04<br \/>\n17.651 &#8211; 12.04 = 5.611<\/p>\n<p>Explanation:<br \/>\n17.651<span style=\"text-decoration: underline;\"><br \/>\n(-)12.040<br \/>\n05.611<br \/>\n<\/span>We subtract each digit according to their place unit values.<\/p>\n<p>Question 36.<br \/>\n19.255 &#8211; 6.194<br \/>\n19.255 &#8211; 6.194 = 13.061<\/p>\n<p>Explanation:<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a015<\/span><br \/>\n19.255<span style=\"text-decoration: underline;\"><br \/>\n(-)06.194<br \/>\n13.061<br \/>\n<\/span>We subtract each digit according to their place unit values.<\/p>\n<p>Question 37.<br \/>\n56.217 &#8211; 35.8<br \/>\n56.217 &#8211; 35.8 = 20.417<\/p>\n<p>Explanation:<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 12<\/span><br \/>\n56.217<span style=\"text-decoration: underline;\"><br \/>\n(-)35.800<br \/>\n20.417<br \/>\n<\/span>We subtract each digit according to their place unit values.<\/p>\n<p>Question 38.<br \/>\n62.486 &#8211; 18.549<br \/>\n62.486 &#8211; 18.549 =\u00a0 43.937<\/p>\n<p>Explanation:<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a011, 14, 16\u00a0\u00a0<\/span><br \/>\n62.486<span style=\"text-decoration: underline;\"><br \/>\n(-)18.549<br \/>\n43.937<br \/>\n<\/span>We subtract each digit according to their place unit values.<\/p>\n<p>Question 39.<br \/>\n152.883 &#8211; 35.6247<br \/>\n152.883 &#8211; 35.6247 = 117.2583<\/p>\n<p>Explanation:<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 4,12,7,12,10\u00a0\u00a0<\/span><br \/>\n152.8830<span style=\"text-decoration: underline;\"><br \/>\n(-) 035.6247<br \/>\n117.2583<br \/>\n<\/span>We subtract each digit according to their place unit values.<\/p>\n<p>Question 40.<br \/>\n129.343 &#8211; 125.0372<br \/>\n129.343 &#8211; 125.0372 = 4.3058<\/p>\n<p>Explanation:<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a012,10\u00a0\u00a0<\/span><br \/>\n129.3430<span style=\"text-decoration: underline;\"><br \/>\n(-)125.0372<br \/>\n4.3058<br \/>\n<\/span>We subtract each digit according to their place unit values.<\/p>\n<p><strong>YOU BE THE TEACHER<\/strong><br \/>\n<strong>Your friend \ufb01nds the sum or difference. Is your friend correct? Explain your reasoning.<\/strong><\/p>\n<p>Question 41.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27309\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-239.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 239\" width=\"133\" height=\"120\" \/><br \/>\nYes, Friend is correct as the sum is 10.008<\/p>\n<p>Explanatation:<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 1,1\u00a0 \u00a0\u00a0<\/span><br \/>\n6.058<br \/>\n<span style=\"text-decoration: underline;\">+3.950<br \/>\n10.008<br \/>\n<\/span>Friend aslo got the same value so friend is<br \/>\ncorrect as 6.058 + 3.950 = 10.008.<\/p>\n<p>Question 42.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27310\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-240.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 240\" width=\"138\" height=\"120\" \/><br \/>\nNo, Friend is incorrect as the difference is 2.32 \u2260 2.48<\/p>\n<p>Explanation:<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a04,10\u00a0 \u00a0\u00a0<\/span><br \/>\n9.50<br \/>\n<span style=\"text-decoration: underline;\">-7.18<br \/>\n2.32<br \/>\n<\/span>Friend got different value so incorrect as<br \/>\n9.50 &#8211; 7.18 = 2.32 \u2260 2.48.<\/p>\n<p>Question 43.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nVehicles must weigh no more than 10.75 tons to cross a bridge.<br \/>\nA truck weighs 11.638 tons. By how many tons does the truck<br \/>\nexceed the weight limit?<br \/>\n0.888 ton weigh is the truck exceed the weight limit<\/p>\n<p>Explanation:<br \/>\nGiven vehicles must weigh no more than 10.75 tons to cross a bridge.<br \/>\nA truck weighs 11.638 tons. So truck weighs more,<br \/>\nwe calculate the difference as<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a015,13\u00a0\u00a0<\/span><br \/>\n11.638<br \/>\n<span style=\"text-decoration: underline;\">-10.750<br \/>\n0.888\u00a0<\/span><\/p>\n<p>Therefore by 0.888 ton weighs is the truck exceed the weight limit.<\/p>\n<p><strong>ADDING AND SUBTRACTING DECIMALS<\/strong><br \/>\n<strong>Evaluate the expression.<\/strong><\/p>\n<p>Question 44.<br \/>\n6.105 + 10.4 + 3.075<br \/>\n6.105 + 10.4 + 3.075 = 19.58<\/p>\n<p>Explanation:<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a01\u00a0\u00a0<\/span><br \/>\n6.105<br \/>\n10.400<br \/>\n<span style=\"text-decoration: underline;\">+3.075<br \/>\n19.580<br \/>\n<\/span>We add digit according to the place values.<\/p>\n<p>Question 45.<br \/>\n22.6 &#8211; 12.286 &#8211; 3.542<br \/>\n22.6 &#8211; 12.286 &#8211; 3.542 = 6.772<\/p>\n<p>Explanation:<br \/>\nFirst we subtract 12.286 from 22.6 as<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a05,9,10\u00a0<\/span><br \/>\n22.600<br \/>\n<span style=\"text-decoration: underline;\">-12.286<br \/>\n10.314<br \/>\n<\/span>Now we subtract 3.542 from 10.314 as<span style=\"text-decoration: underline;\"><br \/>\n9,12,11<br \/>\n<\/span>10.314<span style=\"text-decoration: underline;\"><br \/>\n-3.542<br \/>\n6.772<br \/>\n<\/span>Therefore 22.6 &#8211; 12.286 &#8211; 3.542 = 6.772.<\/p>\n<p>Question 46.<br \/>\n15.35 + 7.604 &#8211; 12.954<br \/>\n15.35 + 7.604 &#8211; 12.954 = 10<\/p>\n<p>Explanation:<br \/>\nFirst we add 15.350 + 7.604 as<\/p>\n<p><u>\u00a01\u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0<\/u><br \/>\n15.350<br \/>\n<span style=\"text-decoration: underline;\">+7.604<br \/>\n22.954<br \/>\n<\/span>Now we subtract 12.954 from 22.954 as<br \/>\n22.954<br \/>\n<span style=\"text-decoration: underline;\">-12.954<br \/>\n10.000<br \/>\n<\/span>Therefore 15.35 + 7.604 &#8211; 12.954 = 10.<\/p>\n<p>Question 47.<br \/>\n16.5 &#8211; 13.45 + 7.293<br \/>\n16.5 &#8211; 13.45 + 7.293 = 10.343<\/p>\n<p>Explanation:<br \/>\nFirst we subtract 13.45 from 16.5 as<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 4,10\u00a0<\/span><br \/>\n16.500<br \/>\n<span style=\"text-decoration: underline;\">-13.450<br \/>\n03.050<br \/>\n<\/span>Now we add 3.05 with 7.293 as<br \/>\n<span style=\"text-decoration: underline;\">1, 1\u00a0 \u00a0 \u00a0<\/span><br \/>\n3.050<br \/>\n<span style=\"text-decoration: underline;\">+7.293<br \/>\n10.343<br \/>\n<\/span>Therefore 16.5 &#8211; 13.45 + 7.293 = 10.343.<\/p>\n<p>question 48.<br \/>\n25.92 &#8211; 18.478 + 8.164<br \/>\n25.92 &#8211; 18.478 + 8.164 = 15.606<\/p>\n<p>Explanation:<br \/>\nFirst we subtract 18.478 from 25.920 as<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 15, 11,10\u00a0<\/span><br \/>\n25.920<br \/>\n<span style=\"text-decoration: underline;\">-18.478<br \/>\n7.442<br \/>\n<\/span>Now we add 7.442 with 8.164 as<br \/>\n<span style=\"text-decoration: underline;\">1,\u00a0 \u00a01\u00a0 \u00a0 \u00a0<\/span><br \/>\n7.442<br \/>\n<span style=\"text-decoration: underline;\">+8.164<br \/>\n15.606<br \/>\n<\/span>Therefore 25.92 &#8211; 18.478 + 8.164 = 15.606.<\/p>\n<p>Question 49.<br \/>\n23.45 + 17.75 &#8211; 19.618<br \/>\n23.45 + 17.75 &#8211; 19.618 = 21.582<\/p>\n<p>Explanation:<br \/>\nFirst we add 23.45 and 17.75 as<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 1,1,1\u00a0\u00a0<\/span><br \/>\n23.45<br \/>\n<span style=\"text-decoration: underline;\">+17.75<br \/>\n41.20<br \/>\nNow we subtract 19.618 from 41.200 as<br \/>\n3,10,11,9,10<br \/>\n41.200<br \/>\n-19.618<br \/>\n21.582<br \/>\n<\/span>Therefore 23.45 + 17.75 &#8211; 19.618 = 21.582.<\/p>\n<p>Question 50.<br \/>\n14.549 &#8211; (8.131 + 3.7024)<br \/>\n14.549 &#8211; (8.131 + 3.7024) = 2.7156<\/p>\n<p>Explanation:<br \/>\nFirst we add (8.131 + 3.7024 ) as<br \/>\n<span style=\"text-decoration: underline;\">1\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span><br \/>\n8.1310<br \/>\n<span style=\"text-decoration: underline;\">+3.7024<br \/>\n11.8334<br \/>\n<\/span>Now we subtract 11.8334 from 14.549 as<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 3,15, 8,10<\/span><br \/>\n14.5490<br \/>\n<span style=\"text-decoration: underline;\">-11.8334<br \/>\n2.7156<br \/>\n<\/span>Therefore 14.549 &#8211; (8.131 + 3.7024) = 2.7156.<\/p>\n<p>Question 51.<br \/>\n41.563 &#8211; (18.65 + 15.9214) + 9.6<br \/>\n41.563 &#8211; (18.65 + 15.9214) + 9.16 =16.5916<\/p>\n<p>Explanation:<br \/>\nFirst we add (8.131 + 3.7024 ) as<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a01,1\u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span><br \/>\n18.6500<br \/>\n<span style=\"text-decoration: underline;\">+15.9214<br \/>\n34.5714<br \/>\n<\/span>Now we subtract 34.5714 from 41.563 as<br \/>\n<span style=\"text-decoration: underline;\">\u00a010,14,16,10<\/span><br \/>\n41.5630<br \/>\n<span style=\"text-decoration: underline;\">-34.5714<br \/>\n6.9916<br \/>\n<\/span>Now we add 6.9916 and 9.6 as<br \/>\n<span style=\"text-decoration: underline;\">1,1<br \/>\n<\/span>\u00a0 6.9916<span style=\"text-decoration: underline;\"><br \/>\n+9.6000<br \/>\n16.5916<br \/>\n<\/span>Therefore 41.563 &#8211; (18.65 + 15.9214) + 9.16 =16.5916.<\/p>\n<p>Question 52.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nA day-care center is building a new outdoor play area.<br \/>\nThe diagram shows the dimensions in meters. How much<br \/>\nfencing is needed to enclose the play area?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27311\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-241.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 241\" width=\"182\" height=\"138\" \/><br \/>\n34.995 meters fencing is needed to enclose the play area.<\/p>\n<p>Explanation:<br \/>\nGiven sides of the outdoor play area, Fencing needed is<br \/>\nsum of the all three sides, So 10.6 + 11.845 + 12.55,<br \/>\n10.600<br \/>\n11.845<br \/>\n+12.550<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 1<br \/>\n34. 995<br \/>\n<\/span>therefore 34.995 meters fencing is needed to enclose the play area.<\/p>\n<p>Question 53.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nOn a fantasy football team, a tight end scores 11.15 points and a<br \/>\nrunning back scores 11.75 points. A wide receiver scores 1.05 points<br \/>\nless than the running back. How many total points do the three players score?<\/p>\n<p>33.6 points all the three players score,<\/p>\n<p>Explanation:<br \/>\nGiven a tight end scores 11.15 points and a<br \/>\nrunning back scores 11.75 points. A wide receiver scores 1.05 points<br \/>\nless than the running back. So a wide receiver scores 11.75 &#8211; 1.05 point,<br \/>\n11.75<br \/>\n<span style=\"text-decoration: underline;\">-1.05<br \/>\n10.70<br \/>\n<\/span>So a wide receiver scores 10.70 points,<br \/>\nNow total points do the three players score are<br \/>\n11.15<br \/>\n11.75<span style=\"text-decoration: underline;\"><br \/>\n<\/span>+10.70<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 1\u00a0 1<br \/>\n33.60<br \/>\n<\/span>Therefore 33.6 points all the three players score.<\/p>\n<p><strong>MODELING REAL LIFE<\/strong><br \/>\nAn astronomical unit (AU) is the average distance between Earth and the Sun. In Exercises 54\u201357, use the table that shows the average distance of each planet in our solar system from the Sun.<\/p>\n<p>Question 54.<br \/>\nHow much farther is Jupiter from the Sun than Mercury?<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27312\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-242.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 242\" width=\"366\" height=\"340\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-242.png 366w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-242-300x279.png 300w\" sizes=\"(max-width: 366px) 100vw, 366px\" \/><br \/>\n4.816 AU farther is Jupiter from the Sun than Mercury,<\/p>\n<p>Explanation:<br \/>\nGiven 5.203 AU is Jupiter average distance from the sun and<br \/>\nmercury is 0.387 AU, Now farther distance Jupiter from<br \/>\nthe sun than mercury is<br \/>\n<span style=\"text-decoration: underline;\">\u00a04,11,9,13\u00a0 \u00a0<\/span><br \/>\n5.203<br \/>\n<span style=\"text-decoration: underline;\">-0.387<br \/>\n4.816<br \/>\n<\/span>Therefore 4.816 AU farther is Jupiter from the Sun than Mercury.<\/p>\n<p>Question 55.<br \/>\nHow much farther is Neptune from the Sun than Mars?<br \/>\n28.546 AU farther is Neptune from the Sun than Mars,<\/p>\n<p>Explanation:<br \/>\nGiven 30.07 AU is Neptune average distance from the sun and<br \/>\nmars is 1.524 AU, Now farther distance Neptune from<br \/>\nthe sun than mars is<br \/>\n<span style=\"text-decoration: underline;\">2, 9,10,6,10\u00a0\u00a0<\/span><br \/>\n30.070<br \/>\n<span style=\"text-decoration: underline;\">-1.524<br \/>\n28.546<br \/>\n<\/span>Therefore 28.546 AU farther is Neptune from the Sun than Mars.<\/p>\n<p>Question 56.<br \/>\nEstimate the greatest distance between Earth and Uranus.<br \/>\n20.189 AU is the greatest distance between Earth and Uranus,<\/p>\n<p>Explanation:<br \/>\nGiven 1.000 AU is earth average distance from the sun and<br \/>\nUranus is 19.189 AU, Now the greatest distance between earth<br \/>\nand Uranus, is<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 1\u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0<\/span><br \/>\n1.000<br \/>\n<span style=\"text-decoration: underline;\">+19.189<br \/>\n20.189<br \/>\n<\/span>Therefore 20.189 AU is the greatest distance between Earth and Uranus.<\/p>\n<p>Question 57.<br \/>\nEstimate the greatest distance between Venus and Saturn.<br \/>\n10.26 AU is the greatest distance between Venus and Saturn,<\/p>\n<p>Explanation:<br \/>\nGiven 0.723 AU is the Venus average distance from the sun and<br \/>\nSaturn is 9.537 AU, Now the greatest distance between Venus<br \/>\nand Saturn, is<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a01,\u00a0 1\u00a0 \u00a0<\/span><br \/>\n0.723<br \/>\n<span style=\"text-decoration: underline;\">+9.537<br \/>\n10.260<br \/>\n<\/span>Therefore 10.26 AU is the greatest distance between Venus and Saturn.<\/p>\n<p>Question 58.<br \/>\n<strong>STRUCTURE<\/strong><br \/>\nWhen is the sum of two decimals equal to a whole number?<br \/>\nWhen is the difference of two decimals equal to a whole number? Explain.<\/p>\n<p>The sum of two decimal numbers is a whole number if the<br \/>\nsum of two fractions can be simplified to a whole number.<br \/>\nor this will happen if the fractional parts of the numbers sum to 1.<\/p>\n<p>The difference of two decimal numbers\u00a0(real\u00a0numbers<br \/>\nwritten in\u00a0decimal digit expansion form) will be an whole number<br \/>\nif and only if their fractional parts are equal and<br \/>\nany whole numbers a &amp; b, a should be always greater or<br \/>\nequal to b then only a-b will be whole number.<\/p>\n<p>Explanation:<br \/>\nWhen we do adding both numbers the fractional parts of the<br \/>\nnumbers so become whole example 1.5 and 3.5 when we add we<br \/>\nget 5 which is a whole number.<\/p>\n<p>In difference example we take 1.17 subtract from 4.17,<br \/>\nhere fractional parts are equal 0.17 respectively, we get<br \/>\nthe\u00a0 difference as 4.17 -1.17 = 3 which is whole number.<\/p>\n<h3><a id=\"Lesson_2.5_Multiplying_Decimals\"><\/a>Lesson 2.5 Multiplying Decimals<\/h3>\n<p><strong>EXPLORATION 1<\/strong><br \/>\n<strong>Multiplying Decimals<\/strong><br \/>\n<strong>Work with a partner.<\/strong><br \/>\na. Write the multiplication expression represented by each area model. Then \ufb01nd the product. Explain how you found your answer.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27276\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-243.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 243\" width=\"685\" height=\"381\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-243.png 685w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-243-300x167.png 300w\" sizes=\"(max-width: 685px) 100vw, 685px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27277\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-244.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 2 Fractions and Decimals 244\" width=\"395\" height=\"191\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-244.png 395w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-2-Fractions-and-Decimals-244-300x145.png 300w\" sizes=\"(max-width: 395px) 100vw, 395px\" \/><br \/>\nb. How can you \ufb01nd the products in part(a) without using a model? How do you know where to place the decimal points in the answers?<br \/>\nc. Find the product of 0.55 and 0.45. Explain how you found your answer.<\/p>\n<p>a. i. The multiplication expression is \\(\\frac{5}{10}\\) X \\(\\frac{8}{10}\\),<br \/>\nThe product is \\(\\frac{40}{100}\\),<br \/>\nii. The multiplication expression is \\(\\frac{9}{10}\\) X \\(\\frac{4}{10}\\),<br \/>\nThe product is \\(\\frac{36}{100}\\),<br \/>\niii. The multiplication expression of whole part is<br \/>\n\\(\\frac{10}{10}\\) X \\(\\frac{5}{10}\\) and<br \/>\ndecimal part is \\(\\frac{5}{10}\\) X \\(\\frac{5}{10}\\)<br \/>\nthen the product results is \\(\\frac{50}{100}\\) + \\(\\frac{25}{100}\\),<br \/>\niv. The multiplication expression of whole part is<br \/>\n\\(\\frac{10}{10}\\) X \\(\\frac{7}{10}\\) and<br \/>\ndecimal part is \\(\\frac{7}{10}\\) X \\(\\frac{7}{10}\\)<br \/>\nthen the product results is \\(\\frac{70}{100}\\) + \\(\\frac{49}{100}\\),<br \/>\nc. The product of\u00a00.55 and 0.45 is 0.2475,<\/p>\n<p>Explanation:<br \/>\na. i. By counting the blocks in the area model found<br \/>\nthe multiplication expression as \\(\\frac{5}{10}\\) X \\(\\frac{8}{10}\\)<br \/>\nand Step I: We multiply the numerators as 5 X 8 = 40<br \/>\nStep II: We multiply the denominators as 10 X 10 =100<br \/>\nStep III: We write the fraction in the simplest form as<br \/>\n\\(\\frac{40}{100}\\), So \\(\\frac{5 X 8}{10 X 10}\\) = \\(\\frac{40}{100}\\).<br \/>\nIf we see the area model the purple color blocks show<br \/>\n40 out of 100 blocks.<br \/>\nii. By counting the blocks in the area model found<br \/>\nthe multiplication expression as \\(\\frac{9}{10}\\) X \\(\\frac{4}{10}\\)<br \/>\nand Step I: We multiply the numerators as 9 X 4 = 36<br \/>\nStep II: We multiply the denominators as 10 X 10 =100<br \/>\nStep III: We write the fraction in the simplest form as<br \/>\n\\(\\frac{36}{100}\\), So \\(\\frac{10 X 10}{10 X 10}\\) = \\(\\frac{36}{100}\\).<br \/>\nIf we see the area model the purple color blocks show<br \/>\n36 out of 100 blocks.<br \/>\niii. By counting the blocks in the area model found<br \/>\nthe multiplication expression as \\(\\frac{10}{10}\\) X \\(\\frac{5}{10}\\)<br \/>\nand Step I: We multiply the numerators as 10 X 5 = 50<br \/>\nStep II: We multiply the denominators as 10 X 10 =100<br \/>\nStep III: We write the fraction in the simplest form as<br \/>\n\\(\\frac{50}{100}\\), So \\(\\frac{10 X 5}{10 X 10}\\) = \\(\\frac{50}{100}\\).<br \/>\nNow in decimal part we have \\(\\frac{5}{10}\\) X \\(\\frac{5}{10}\\),<br \/>\nsimilar to whole part we do multiplication<br \/>\nStep I: We multiply the numerators as 5 X 5 = 25<br \/>\nStep II: We multiply the denominators as 10 X 10 =100<br \/>\nStep III: We write the fraction in the simplest form as<br \/>\n\\(\\frac{25}{100}\\), therefore then the product results is<br \/>\n\\(\\frac{50}{100}\\) + \\(\\frac{25}{100}\\),<br \/>\niv. By counting the blocks in the area model found<br \/>\nthe multiplication expression as \\(\\frac{10}{10}\\) X \\(\\frac{7}{10}\\)<br \/>\nand Step I: We multiply the numerators as 10 X 7 = 70<br \/>\nStep II: We multiply the denominators as 10 X 10 =100<br \/>\nStep III: We write the fraction in the simplest form as<br \/>\n\\(\\frac{70}{100}\\), So \\(\\frac{10 X 7}{10 X 10}\\) = \\(\\frac{70}{100}\\).<br \/>\nNow in decimal part we have \\(\\frac{7}{10}\\) X \\(\\frac{7}{10}\\),<br \/>\nsimilar to whole part we do multiplication<br \/>\nStep I: We multiply the numerators as 7 X 7 = 49<br \/>\nStep II: We multiply the denominators as 10 X 10 =100<br \/>\nStep III: We write the fraction in the simplest form as<br \/>\n\\(\\frac{49}{100}\\), therefore then the product results is<br \/>\n\\(\\frac{70}{100}\\) + \\(\\frac{49}{100}\\).<\/p>\n<p>b. We use normal multiplication of numbers without any model,<br \/>\nDecimals\u00a0are a shorthand way to write fractions and<br \/>\nmixed numbers with denominators that are powers of 10, like\u00a0<span id=\"MathJax-Element-2-Frame\" class=\"MathJax\" style=\"font-style: normal; font-weight: normal; line-height: normal; font-size: 16px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px;\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mn&gt;10&lt;\/mn&gt;&lt;mo&gt;,&lt;\/mo&gt;&lt;mn&gt;100&lt;\/mn&gt;&lt;mo&gt;,&lt;\/mo&gt;&lt;mn&gt;1000&lt;\/mn&gt;&lt;mo&gt;,&lt;\/mo&gt;&lt;mn&gt;10000&lt;\/mn&gt;&lt;mo&gt;,&lt;\/mo&gt;&lt;\/math&gt;\"><span id=\"MathJax-Span-4\" class=\"math\" role=\"math\"><span id=\"MathJax-Span-5\" class=\"mrow\"><span id=\"MathJax-Span-6\" class=\"mn\">10<\/span><span id=\"MathJax-Span-7\" class=\"mo\">,<\/span><span id=\"MathJax-Span-8\" class=\"mn\">100<\/span><span id=\"MathJax-Span-9\" class=\"mo\">,<\/span><span id=\"MathJax-Span-10\" class=\"mn\">1000<\/span><span id=\"MathJax-Span-11\" class=\"mo\">,<\/span><span id=\"MathJax-Span-12\" class=\"mn\">10000<\/span><span id=\"MathJax-Span-13\" class=\"mo\">,<\/span><\/span><\/span><\/span><\/p>\n<p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mn>10<\/mn><mo>,<\/mo><mn>100<\/mn><mo>,<\/mo><mn>1000<\/mn><mo>,<\/mo><mn>10000<\/mn><mo>,<\/mo><\/math><\/p>\n<p>etc.<br \/>\nIf a number has a\u00a0decimal point, then the first digit to the<br \/>\nright of the decimal point indicates the number of tenths.<\/p>\n<p>For example, the decimal\u00a0<span id=\"MathJax-Element-3-Frame\" class=\"MathJax\" style=\"font-style: normal; font-weight: normal; line-height: normal; font-size: 16px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px;\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mn&gt;0.3&lt;\/mn&gt;&lt;\/math&gt;\"><span id=\"MathJax-Span-14\" class=\"math\" role=\"math\"><span id=\"MathJax-Span-15\" class=\"mrow\"><span id=\"MathJax-Span-16\" class=\"mn\">0.3<\/span><\/span><\/span><\/span> is the same as the fraction \\(\\frac{3}{10}\\)<br \/>\nThe second digit to the right of the decimal point indicates<br \/>\nthe number of hundredths.<\/p>\n<p>For example, the decimal\u00a0<span id=\"MathJax-Element-5-Frame\" class=\"MathJax\" style=\"font-style: normal; font-weight: normal; line-height: normal; font-size: 16px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px;\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mn&gt;3.26&lt;\/mn&gt;&lt;\/math&gt;\"><span id=\"MathJax-Span-23\" class=\"math\" role=\"math\"><span id=\"MathJax-Span-24\" class=\"mrow\"><span id=\"MathJax-Span-25\" class=\"mn\">3.26 <\/span><\/span><\/span><\/span>is the same as the mixed number<br \/>\n3 \\(\\frac{26}{100}\\) . (Note that the first digit to the left\u00a0of<br \/>\nthe decimal point is the ones digit.)<\/p>\n<p>We can write decimals with many places to the right of the decimal point.<br \/>\nAs shown in below example<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-51794\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-64.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-64\" width=\"291\" height=\"197\" \/><br \/>\nc. The product of 0.55 and 0.45 is<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a02\u00a0 \u00a0<\/span><br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a02\u00a0 \u00a0\u00a0<\/span><br \/>\n0.55&#8212;&#8212;&#8212;&#8212;&#8211; 2 decimal places<br \/>\n<span style=\"text-decoration: underline;\">X0.45<\/span> &#8212;&#8212;&#8212;&#8212; 2 decimal places<br \/>\n0275\u00a0 \u00a0 \u00a0 \u00a0 \u00a0(first 0.05 X 0.55)<br \/>\n<span style=\"text-decoration: underline;\">2200\u00a0 \u00a0 <\/span>\u00a0 \u00a0 \u00a0(0.4 X 0.55)<br \/>\n<span style=\"text-decoration: underline;\">0.2475\u00a0<\/span>&#8212;&#8212;&#8212;- 4 decimal places<\/p>\n<p>Therefore the product of 0.55 and 0.45 is 0.2475.<\/p>\n<p><strong>2.5 Lesson<\/strong><\/p>\n<p><strong>Key Idea<\/strong><br \/>\n<strong>Multiplying Decimals by Whole Numbers<\/strong><br \/>\n<strong>Words<\/strong><br \/>\nMultiply as you would with whole numbers. Then count the number of decimal places in the decimal factor. The product has the same number of decimal places.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27313\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-245.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 245\" width=\"515\" height=\"76\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-245.png 515w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-245-300x44.png 300w\" sizes=\"(max-width: 515px) 100vw, 515px\" \/><\/p>\n<p><strong>Try It<\/strong><br \/>\n<strong>Multiply. Use estimation to check your answer.<\/strong><\/p>\n<p>Question 1.<br \/>\n12.3 \u00d7 8<br \/>\n12.3 X 8 = 98.4<br \/>\nIs not reasonable 96 \u2260 \u2248 98,<\/p>\n<p>Explanation:<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 2\u00a0 \u00a0\u00a0<\/span><br \/>\n12.3\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 1 decimal place<br \/>\n<span style=\"text-decoration: underline;\">X\u00a0 8<br \/>\n98.4\u00a0\u00a0<\/span><br \/>\nEstimate : 12 X 8 = 96,<br \/>\nReasonable 98.4 \u2248 98,<br \/>\nIs not reasonable 96 \u2260 \u2248 98.<\/p>\n<p>Question 2.<br \/>\n5 \u00d7 14.51<br \/>\n5 \u00d7 14.51 = 72.55<br \/>\nIs not reasonable 75 \u2260 \u2248 73.<\/p>\n<p>Explanation:<br \/>\n<span style=\"text-decoration: underline;\">2,2\u00a0 \u00a0\u00a0<\/span><br \/>\n14.51\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 2 decimal places<br \/>\n<span style=\"text-decoration: underline;\">X\u00a0 \u00a05<br \/>\n72.55\u00a0 \u00a0 \u00a0<\/span><br \/>\nEstimate : 5 X 15 = 75,<br \/>\nReasonable 72.55 \u2248 73,<br \/>\nIs not reasonable 75 \u2260 \u2248 73.<\/p>\n<p>Question 3.<br \/>\n2.3275 X 90<br \/>\n2.3275 X 90 = 209.475<br \/>\nIs not reasonable 180 \u2260 \u2248 210.<\/p>\n<p>Explanation:<br \/>\n<span style=\"text-decoration: underline;\">2,4\u00a0 \u00a0\u00a0<\/span><br \/>\n2.3275\u00a0 \u00a0 \u00a0 4 decimal places<br \/>\n<span style=\"text-decoration: underline;\">X\u00a0 \u00a0 90<br \/>\n<\/span>0000000<br \/>\n<span style=\"text-decoration: underline;\">209475<br \/>\n209.4750<\/span><br \/>\nEstimate : 2 X 90 = 180,<br \/>\nReasonable 209.4750 \u2248 210,<br \/>\nIs not reasonable 180 \u2260 \u2248 210.<\/p>\n<p>The rule for multiplying two decimals is similar to the rule for multiplying a decimal by a whole number.<\/p>\n<p><strong>Key Idea<\/strong><br \/>\n<strong>Multiplying Decimals by Decimals<\/strong><br \/>\n<strong>Words<\/strong><br \/>\nMultiply as you would with whole numbers. Then add the number of decimal places in the factors. The sum is the number of decimal places in the product.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27314\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-246.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 246\" width=\"311\" height=\"76\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-246.png 311w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-246-300x73.png 300w\" sizes=\"(max-width: 311px) 100vw, 311px\" \/><\/p>\n<p><strong>Try It<\/strong><br \/>\n<strong>Multiply. Use estimation to check your answer.<\/strong><\/p>\n<p>Question 5.<br \/>\n8.1 \u00d7 5.6<br \/>\n8.1 \u00d7 5.6 = 45.36<br \/>\nIs not reasonable 45 \u2260 \u2248 48,<\/p>\n<p>Explanation:<br \/>\n8.1 &#8212;&#8212;-1 decimal place<br \/>\n<span style=\"text-decoration: underline;\">X 5.6 &#8212;&#8211;1 decimal place<br \/>\n<\/span>\u00a0 \u00a0486\u00a0\u00a0<span style=\"text-decoration: underline;\"><br \/>\n4050<br \/>\n45.36\u00a0 \u00a0&#8212;&#8211; 2 decimal places<br \/>\n<\/span>Estimate : 8 X 6 = 48,<br \/>\nReasonable 45.36 \u2248 45,<br \/>\nIs not reasonable 45 \u2260 \u2248 48.<\/p>\n<p>Question 6.<br \/>\n2.7 \u00d7 9.04<br \/>\n2.7 \u00d7 9.04 = 24.408<br \/>\nIs not reasonable 24 \u2260 \u2248 27,<\/p>\n<p>Explanation:<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 2\u00a0 \u00a0\u00a0<\/span><br \/>\n9.04 &#8212;&#8212;-2 decimal places<br \/>\n<span style=\"text-decoration: underline;\">X 2.7 &#8212;&#8212;1 decimal places<br \/>\n<\/span>\u00a0 \u00a06328<span style=\"text-decoration: underline;\"><br \/>\n18080<br \/>\n24.408\u00a0 \u00a0&#8212;&#8211; 3 decimal places<br \/>\n<\/span>Estimate : 3 X 9 = 27,<br \/>\nReasonable 24.408 \u2248 24,<br \/>\nIs not reasonable 24 \u2260 \u2248 27.<\/p>\n<p>Question 7.<br \/>\n6.32 \u00d7 0.09<br \/>\n6.32 \u00d7 0.09 = 0.5688<br \/>\nIs reasonable 0.6 = 0.6<\/p>\n<p>Explanation:<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 2,1\u00a0 \u00a0\u00a0<\/span><br \/>\n6.32 &#8212;&#8212;-2 decimal places<br \/>\n<span style=\"text-decoration: underline;\">X 0.09 &#8212;&#8212;2 decimal places<br \/>\n<\/span><span style=\"text-decoration: underline;\">0.5688\u00a0&#8212;&#8211; 4 decimal places<br \/>\n<\/span>Estimate : 6 X 0.1 = 0.6,<br \/>\nReasonable 0.5688\u2248 0.6,<br \/>\nIs reasonable 0.6= 0.6.<\/p>\n<p>Question 8.<br \/>\n1.785 \u00d7 0.2<br \/>\n1.785 \u00d7 0.2 = 0.357<br \/>\nIs reasonable 0.4= 0.4,<\/p>\n<p>Explanation:<br \/>\n<span style=\"text-decoration: underline;\">1,1,1\u00a0 \u00a0\u00a0<\/span><br \/>\n1.785 &#8212;&#8212;-3 decimal places<br \/>\n<span style=\"text-decoration: underline;\">X 0.2 &#8212;&#8212;\u00a0 1 decimal places<br \/>\n<\/span><span style=\"text-decoration: underline;\">0.3570&#8212;&#8211; 4 decimal places<br \/>\n<\/span>Estimate : 2 X 0.2 = 0.4,<br \/>\nReasonable 0.3570\u2248 0.4,<br \/>\nIs reasonable 0.4= 0.4.<\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><br \/>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p><strong>EVALUATING AN EXPRESSION<\/strong><br \/>\n<strong>Evaluate the expression.<\/strong><\/p>\n<p>Question 11.<br \/>\n8 \u00d7 11.215<br \/>\n8 \u00d7 11.215 = 89.72<\/p>\n<p>Explanation:<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 1,\u00a0 \u00a04\u00a0 \u00a0<\/span><br \/>\n11.215 &#8212;&#8211; 3 decimal places<br \/>\n<span style=\"text-decoration: underline;\">X 8<br \/>\n89.720&#8212;&#8212; 3 decimal places<br \/>\n<\/span>Therefore, 8 \u00d7 11.215 = 89.72<\/p>\n<p>Question 12.<br \/>\n9.42 . 6.83<br \/>\n9.42 X 6.83 = 64.3386<\/p>\n<p>Explanation:<br \/>\n5,1<br \/>\n3,1<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 1,\u00a0 \u00a0 \u00a0<\/span><br \/>\n9.42 &#8212;&#8211; 2 decimal places<br \/>\n<span style=\"text-decoration: underline;\">X6.83 &#8212;&#8212;2 decimal places<br \/>\n<\/span>002826<br \/>\n075360<br \/>\n<span style=\"text-decoration: underline;\">565200<br \/>\n64.3386&#8212;&#8212; 4 decimal places<br \/>\n<\/span>Therefore, 9.42 X 6.83 = 64.3386<\/p>\n<p>Question 13.<br \/>\n0.15(4.3 &#8211; 2.417)<br \/>\n0.15 X (4.3 &#8211; 2.417) = 0.28245<\/p>\n<p>Explanation:<br \/>\nFirst we calculate subtracting 2.417 from 4.3 as<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 12,9,10<\/span><br \/>\n4.300<br \/>\n<span style=\"text-decoration: underline;\">-2.417<br \/>\n1.883<\/span><br \/>\nnow we multiply 0.15 and 1.883 as<br \/>\n4,4,5<br \/>\n1.883&#8212;- 3\u00a0decimal places<br \/>\n<span style=\"text-decoration: underline;\">X 0.15&#8212;-2 decimal places<br \/>\n<\/span>\u00a0 9415<span style=\"text-decoration: underline;\"><br \/>\n18830<br \/>\n0.28245&#8212; 5 decimal places<br \/>\n<\/span>Therefore, 0.15 X (4.3 &#8211; 2.417) = 0.28245.<\/p>\n<p>Question 14.<br \/>\n<strong>NUMBER SENSE<\/strong><br \/>\nIf you know 12 \u00d7 24 = 288, how can you \ufb01nd 0.12 \u00d7 0.24?<br \/>\nWe have 4 deciml places so 0.12 X 0.24 = 0.0288<\/p>\n<p>Explanation:<br \/>\nGiven I know 12 X 24 = 288,<br \/>\nwe find 0.12 X 0.24 as we have 2 + 2 = 4 decimals<br \/>\nwe write 244 with four decimals as 0.0288,<br \/>\ntherefore 0.12 X 0.24 = 0.0288.<\/p>\n<p>Question 15.<br \/>\n<strong>NUMBER SENSE<\/strong><br \/>\nIs the product 1.23 \u00d7 8 greater than or less than 8? Explain.<br \/>\nThe product of 1.23 X 8 is greater than 8,<\/p>\n<p>Explanation:<br \/>\n1.23 X 8 = 9.84,<\/p>\n<p>Now comparing 9.84 with 8, 9.84 is greater than 8,<br \/>\nor we have the whole part 1 plus 0.23 when multiplied by 8 it&#8217;s<br \/>\nvalue becomes more only.<br \/>\ntherefore 1.23 X 8 &gt;8.<\/p>\n<p>Question 16.<br \/>\n<strong>REASONING<\/strong><br \/>\nCopy the problem and place the decimal point in the product.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27315\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-247.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 247\" width=\"70\" height=\"72\" \/><br \/>\n8.722 we have 3 decimal places so<br \/>\n1.78 X 4.9 = 8.722<br \/>\nExplanation:<br \/>\n1.78 &#8212;-2 decimal places<br \/>\n<span style=\"text-decoration: underline;\">X 4.9&#8212;1 decimal place<\/span><br \/>\n<span style=\"text-decoration: underline;\">8.722&#8212;3 decimal places<br \/>\n<\/span>Thefore, 8.722 has decimal point before 3 digits.<\/p>\n<p><strong>Self-Assessment for Problem Solving<\/strong><\/p>\n<p>Solve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 17.<br \/>\nYou earn $9.15 per hour painting a fence. It takes 6.75 hours to paint the fence.<br \/>\nDid you earn enough money to buy the jersey shown? If so, how much money<br \/>\ndo you have left? If not, how much money do you need to earn?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27316\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-248.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 248\" width=\"237\" height=\"170\" \/><\/p>\n<p>Yes, I earned enough money $61.7625 to buy the jersey shown,<br \/>\nMoney left is $1.7725.<\/p>\n<p>Explanation:<br \/>\nGiven I earn $9.15 per hour painting a fence.<br \/>\nIt takes 6.75 hours to paint the fence. So money earned is<br \/>\n$9.15 X 6.75 = $61.7625<br \/>\n<span style=\"text-decoration: underline;\">\u00a03<\/span><br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a03<br \/>\n2\u00a0<\/span><br \/>\n9.15 &#8212;&#8212;2 decimal values<br \/>\n<span style=\"text-decoration: underline;\">X6.75&#8212;&#8211; 2 decimal values<br \/>\n<\/span>\u00a0004575<br \/>\n064050<span style=\"text-decoration: underline;\"><br \/>\n+549000<br \/>\n61.7625&#8212;-4 decimal places<br \/>\n<\/span>Therefore, yes, I earned enough money $61.7625 to buy the<br \/>\njersey shown, because given the cost of jersey&#8217;s is $59.99 each<br \/>\nwhich is less compared to what i have earned.<br \/>\nNow money left is $61.7625 &#8211; $59.99 = $1.7725,<br \/>\n<span style=\"text-decoration: underline;\">\u00a010,16,16<\/span><br \/>\n61.7625<br \/>\n<span style=\"text-decoration: underline;\">-59.9900<\/span><br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a01.7725<\/span><br \/>\nSo, money left is $1.7725.<\/p>\n<p>Question 18.<br \/>\nA sand volleyball court is a rectangle that has a length of 52.5 feet and<br \/>\na width that is half of the length. In case of rain, the court is covered<br \/>\nwith a tarp. How many square feet of tarp are needed to cover the court?<\/p>\n<p>1378.125 square feet of trap is needed to cover the court,<\/p>\n<p>Explanation:<br \/>\nGiven a\u00a0sand volleyball court is a rectangle that has a length<br \/>\nof 52.5 feet and a width that is half of the length means width is<br \/>\n52.5 \u00f7 2 = 26.25 feet, Now to cover the court with a trap we need<br \/>\n52.5 X 26.25 = 1378.125 square feet,<br \/>\n52.5&#8212;&#8212;&#8212;&#8212;2 decimal places<br \/>\n<span style=\"text-decoration: underline;\">X26.25&#8212;&#8212;&#8211; 2 decimal places<br \/>\n<\/span>2625 &#8212;-(52.5 X 0.05)<br \/>\n1050 &#8212;(52.5 X0.2)<br \/>\n31500&#8212;(52.5 X 6)<br \/>\n<span style=\"text-decoration: underline;\">+105000&#8212;(52.5 X20)<\/span><br \/>\n<span style=\"text-decoration: underline;\">1378.0125&#8212;&#8212;4 decimal places<br \/>\n<\/span>Therefore,1378.125 square feet of trap is needed to cover the court.<\/p>\n<p>Question 19.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nYou buy 4 cases of bottled water and 5 bottles of fruit punch for a<br \/>\nbirthday party. Each case of bottled water costs $2.75, and each bottle<br \/>\nof fruit punch costs $1.35. You hand the cashier a $20 bill.<br \/>\nHow much change will you receive?<\/p>\n<p>I will receive $2.25 as a change,<\/p>\n<p>Explanation:<br \/>\nGiven I buy 4 cases of bottled water and 5 bottles of fruit punch for a<br \/>\nbirthday party. Each case of bottled water costs $2.75, and each bottle<br \/>\nof fruit punch costs $1.35, Now 4 cases of bottled costs is<br \/>\n4 X $2.75=$11,<br \/>\n<span style=\"text-decoration: underline;\">\u00a030,2\u00a0<\/span><br \/>\n2.75&#8212;&#8212; 2 decimal places<br \/>\n<span style=\"text-decoration: underline;\">x 4<br \/>\n11.00&#8212;&#8212;2 decimal places<br \/>\n<\/span>and 5 bottles of fruit punch costs is 5 X $1.35 = $6.75<br \/>\n<span style=\"text-decoration: underline;\">1,2\u00a0 \u00a0<\/span><br \/>\n1.35&#8212;- 2 decimal places<span style=\"text-decoration: underline;\"><br \/>\nX 5<br \/>\n6.75&#8212;-2 decimal places<br \/>\n<\/span>Now total bill amount is $11 + $ 6.75= $17.75,<br \/>\n11.00<br \/>\n<span style=\"text-decoration: underline;\">+6.75<br \/>\n17.75<br \/>\n<\/span>I hand the cashier $20 , The change I will receive is<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 9,9,10<\/span><br \/>\n20.00<br \/>\n<span style=\"text-decoration: underline;\">-17.75<\/span><br \/>\n<span style=\"text-decoration: underline;\">\u00a0 2.25<br \/>\n<\/span>Therefore, I will receive $2.25 as a change.<\/p>\n<h3><a id=\"Multiplying_Decimals_Homework_&amp;_Practice_2.5\"><\/a>Multiplying Decimals Homework &amp; Practice 2.5<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Add or subtract.<\/strong><\/p>\n<p>Question 1.<br \/>\n12.29 &#8211; 6.15<br \/>\n12.29 &#8211; 6.15 = 6.14<\/p>\n<p>Explanation:<br \/>\n<span style=\"text-decoration: underline;\">\u00a0,12<\/span><br \/>\n12.29<br \/>\n<span style=\"text-decoration: underline;\">-6.15<br \/>\n06.14<br \/>\n<\/span>Therefore, 12.29 &#8211; 6.15 = 6.14.<\/p>\n<p>Question 2.<br \/>\n4.6 + 11.81<br \/>\n4.6 + 11.81 = 16.41<\/p>\n<p>Explanation:<br \/>\n<span style=\"text-decoration: underline;\">\u00a0,\u00a0 \u00a0 1\u00a0 \u00a0\u00a0<\/span><br \/>\n04.60<br \/>\n<span style=\"text-decoration: underline;\">+11.81<br \/>\n16.41<br \/>\n<\/span>Therefore, 4.6 + 11.81 = 16.41.<\/p>\n<p>Question 3.<br \/>\n9.34 + 17.009<br \/>\n9.34 + 17.009 = 26.349<br \/>\nExplanation:<br \/>\n<span style=\"text-decoration: underline;\">\u00a0, 1\u00a0 \u00a0\u00a0<\/span><br \/>\n09.340<br \/>\n<span style=\"text-decoration: underline;\">+17.009<br \/>\n26.349<br \/>\n<\/span>Therefore, 9.34 + 17.009 = 26.349.<\/p>\n<p>Question 4.<br \/>\n18.247 &#8211; 16.262<br \/>\n18.247 &#8211; 16.262 = 1.985<\/p>\n<p>Explanation:<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a011,14<\/span><br \/>\n18.247<br \/>\n<span style=\"text-decoration: underline;\">-16.262<br \/>\n1.985<br \/>\n<\/span>Therefore, 18.247 &#8211; 16.262 = 1.985.<\/p>\n<p><strong>Divide.<\/strong><\/p>\n<p>Question 5.<br \/>\n78 \u00f7 3<br \/>\n78 \u00f7 3 = 26<\/p>\n<p>Explanation:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-51840\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-65.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-65\" width=\"251\" height=\"211\" \/><br \/>\nhere t<span style=\"font-size: 16px;\">he first number 78 is called the dividend<br \/>\nand t<\/span><span style=\"font-size: 16px;\">he second number 3 is called the divisor.<br \/>\nWe will get 0 as remainder and top 26 is the answer,<br \/>\nas shown in the picture, <\/span>Therefore 78 \u00f7 3 = 26.<\/p>\n<p>Question 6.<br \/>\n65 \u00f7 13<br \/>\n65 \u00f7 13 = 5<\/p>\n<p>Explanation:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-51841\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-66.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-66\" width=\"251\" height=\"129\" \/><br \/>\nhere t<span style=\"font-size: 16px;\">he first number 65 is called the dividend<br \/>\nand t<\/span><span style=\"font-size: 16px;\">he second number 13 is called the divisor.<br \/>\nWe will get 0 as remainder and top 5 is the answer<br \/>\nas shown in the picture, <\/span>Therefore 65 \u00f7 13 = 5.<\/p>\n<p>Question 7.<br \/>\n57 \u00f7 19<br \/>\n57 \u00f7 19 = 3<\/p>\n<p>Explanation:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-51845\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-67.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-67\" width=\"152\" height=\"129\" \/> 19 X 3 = 57<br \/>\nhere t<span style=\"font-size: 16px;\">he first number 57 is called the dividend<br \/>\nand t<\/span><span style=\"font-size: 16px;\">he second number 19 is called the divisor.<br \/>\nWe will get 0 as remainder top 3 is the answer<br \/>\nas shown in the picture, <\/span>Therefore 57 \u00f7 19 = 3.<\/p>\n<p>Question 8.<br \/>\n84 \u00f7 12<br \/>\n84 \u00f7 12 = 7<\/p>\n<p>Explanation:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-51849\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-68.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-68\" width=\"252\" height=\"129\" \/><br \/>\nhere t<span style=\"font-size: 16px;\">he first number 84 is called the dividend<br \/>\nand t<\/span><span style=\"font-size: 16px;\">he second number 12 is called the divisor.<br \/>\nWe will get 0 as remainder top 7 is the answer<br \/>\nas shown in the picture, <\/span>Therefore 84 \u00f7 12 = 7.<\/p>\n<p>Question 9.<br \/>\nWhat is <img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27318\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-249.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 249\" width=\"55\" height=\"43\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27318\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-249.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 249\" width=\"55\" height=\"43\" \/> = \\(\\frac{52}{15}\\) = 3\\(\\frac{7}{15}\\)<\/p>\n<p>Explanation:<br \/>\nGiven expression as 4\\(\\frac{1}{3}\\) X \\(\\frac{4}{5}\\) ,<br \/>\nFirst we write mixed fraction as (4 X 3 + 1 by 3) =\\(\\frac{13}{3}\\), ,<br \/>\n\\(\\frac{13}{3}\\) X \\(\\frac{4}{5}\\) =\\(\\frac{13 X 4}{3 X 5}\\) =<br \/>\n\\(\\frac{52}{3}\\) as numerator is greater we write in<br \/>\nmixed fraction as (3 X 15 + 7 by 15) = 3\\(\\frac{7}{15}\\),<br \/>\nTherefore, 4\\(\\frac{1}{3}\\) X \\(\\frac{4}{5}\\) =<br \/>\n\\(\\frac{52}{15}\\) = 3\\(\\frac{7}{15}\\).<\/p>\n<p><strong>Evaluate the expression.<\/strong><\/p>\n<p>Question 10.<br \/>\n4 + 6<sup>2<\/sup> \u00f7 2<br \/>\n4 + 6<sup>2<\/sup> \u00f7 2 = 2<\/p>\n<p>Explanation:<br \/>\nGiven expression as 4 + 6<sup>2<\/sup> \u00f7 2,<br \/>\nfirst we evaluate 6<sup>2 <\/sup>= 6 X 6 = 36, then<br \/>\n4 + 36 = 40, Now 40 \u00f7 2 = 20 (2 X 20 = 40),<br \/>\ntherefore, 4 + 6<sup>2<\/sup> \u00f7 2 = 2.<\/p>\n<p>Question 11.<br \/>\n(35 + 9) \u00f7 4 &#8211; 3<sup>2<br \/>\n<\/sup>(35 + 9) \u00f7 4 &#8211; 3<sup>2 <\/sup>= 2<\/p>\n<p>Explanation:<br \/>\nGiven expression as (35 + 9) \u00f7 4 &#8211; 3<sup>2<\/sup>,<br \/>\nfirst we evaluate 35 + 9 = 44,<br \/>\nthen 44 \u00f7 4\u00a0 = 11 (4 X 11 = 44),<br \/>\nand 11 &#8211; 3<sup>2 <\/sup>= 11 &#8211; (3 X 3) = 11 &#8211; 9 = 2,<br \/>\ntherefore, (35 + 9) \u00f7 4 &#8211; 3<sup>2 <\/sup>= 2.<\/p>\n<p>Question 12.<br \/>\n8<sup>2<\/sup> \u00f7 [(14 &#8211; 12) \u00d7 2<sup>3<\/sup>]<br \/>\n8<sup>2<\/sup> \u00f7 [(14 &#8211; 12) \u00d7 2<sup>3<\/sup>] = 4<\/p>\n<p>Explanation:<br \/>\nGiven expression as 8<sup>2<\/sup> \u00f7 [(14 &#8211; 12) \u00d7 2<sup>3<\/sup>]<br \/>\nFirst we calculate [(14 &#8211; 12) \u00d7 2<sup>3<\/sup>] = (14 -12) X (2 X 2 X 2),<br \/>\n2 X 8 = 16, Now 8<sup>2<\/sup> \u00f7 16 = (8X 8) \u00f7 16 = 64 \u00f7 16 = 4 (16 x 4 =64),<br \/>\ntherefore,8<sup>2<\/sup> \u00f7 [(14 &#8211; 12) \u00d7 2<sup>3<\/sup>] = 4.<\/p>\n<p><strong>Concepts, Skills, &amp; Problem Solving<\/strong><\/p>\n<p><strong>USING TOOLS<\/strong><br \/>\n<strong>Use an area model to \ufb01nd the product.<\/strong> (See Exploration 1, p. 73.)<\/p>\n<p>Question 13.<br \/>\n2.1 \u00d7 1.5<br \/>\n2.1 \u00d7 1.5 = 3.15<br \/>\nExplanation:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-51865\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-69-2.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-69\" width=\"1324\" height=\"443\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-69-2.bmp 1324w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-69-2-300x100.jpg 300w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-69-2-1024x343.jpg 1024w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-69-2-768x257.jpg 768w\" sizes=\"(max-width: 1324px) 100vw, 1324px\" \/><br \/>\n2.1 \u00d7 1.5 = 3.15,<br \/>\nWe took 2 full and 0.1 then multiplied by<br \/>\n1 full and 0.5 we got 3 full and 0.15 as shown in the picture.<\/p>\n<p>Question 14.<br \/>\n0.6 \u00d7 0.4<br \/>\n0.6 X 0.4 = 0.24<\/p>\n<p>Explanation:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-51859\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-70.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-70\" width=\"419\" height=\"238\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-70.bmp 419w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-70-300x170.jpg 300w\" sizes=\"(max-width: 419px) 100vw, 419px\" \/><br \/>\nThe purple color shows the result 0.24.<\/p>\n<p>Question 15.<br \/>\n0.7 \u00d7 0.3<br \/>\n0.7 X 0.3 = 0.21<\/p>\n<p>Explanation:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-51915\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-71-2.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-71\" width=\"415\" height=\"238\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-71-2.bmp 415w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-71-2-300x172.jpg 300w\" sizes=\"(max-width: 415px) 100vw, 415px\" \/><br \/>\nThe purple color shows the result 0.21.<\/p>\n<p>Question 16.<br \/>\n2.7 \u00d7 2.3<br \/>\n2.7 X 2.3 = 6.21<\/p>\n<p>Explanation:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-51868\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-72-2.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-72\" width=\"1340\" height=\"627\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-72-2.bmp 1340w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-72-2-300x140.jpg 300w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-72-2-1024x479.jpg 1024w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-72-2-768x359.jpg 768w\" sizes=\"(max-width: 1340px) 100vw, 1340px\" \/><br \/>\nThe purple color shows the result 6.21.<\/p>\n<p><strong>MULTIPLYING DECIMALS AND WHOLE NUMBERS<\/strong><br \/>\n<strong>Multiply. Use estimation to check your answer.<\/strong><\/p>\n<p>Question 17.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27317\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-249.1.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 249.1\" width=\"49\" height=\"51\" \/><br \/>\n<span style=\"text-decoration: underline;\">33.6<br \/>\n<\/span><br \/>\nExplanation:<br \/>\n<span style=\"text-decoration: underline;\">\u00a05\u00a0 \u00a0<\/span><br \/>\n4.8 &#8212;&#8212;1 decimal place<br \/>\n<span style=\"text-decoration: underline;\">X 7<br \/>\n33.6&#8212;&#8211; 1 decimal place<br \/>\n<\/span>Therefore, 4.8 X 7 = 33.6.<\/p>\n<p>Question 18.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27319\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-250.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 250\" width=\"61\" height=\"58\" \/><br \/>\n<span style=\"text-decoration: underline;\">\u00a0 31.5<\/span><\/p>\n<p>Explanation:<span style=\"text-decoration: underline;\"><br \/>\n1<br \/>\n<\/span>6.3 &#8212;&#8212;1 decimal place<span style=\"text-decoration: underline;\"><br \/>\nX 5<br \/>\n31.5&#8212;&#8211; 1 decimal place<br \/>\n<\/span>Therefore, 6.3 X 5 = 31.5.<\/p>\n<p>Question 19.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27320\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-251.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 251\" width=\"61\" height=\"55\" \/><br \/>\n<span style=\"text-decoration: underline;\">115.04<\/span><\/p>\n<p>Explanation:<br \/>\n<span style=\"text-decoration: underline;\">1, 5\u00a0 \u00a0<\/span><br \/>\n7.19 &#8212;&#8212;2 decimal places<br \/>\n<span style=\"text-decoration: underline;\">X 16<br \/>\n<\/span>4314<br \/>\n<span style=\"text-decoration: underline;\">7190<br \/>\n115.04&#8212;&#8211; 2 decimal places<br \/>\n<\/span>Therefore, 7.19 X 16 = 115.04.<\/p>\n<p>Question 20.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27321\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-252.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 252\" width=\"60\" height=\"53\" \/><br \/>\n<span style=\"text-decoration: underline;\">\u00a0 18.27<\/span><\/p>\n<p>Explanation:<br \/>\n1, 1<br \/>\n0.87 &#8212;&#8212;2 decimal places<span style=\"text-decoration: underline;\"><br \/>\nX 21<br \/>\n<\/span>\u00a0 \u00a0 87<span style=\"text-decoration: underline;\"><br \/>\n1740<br \/>\n18.27&#8212;&#8211; 2 decimal places<br \/>\n<\/span>Therefore, 8.87 X 21 = 18.27.<span style=\"text-decoration: underline;\"><br \/>\n<\/span><\/p>\n<p>Question 21.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27322\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-253.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 253\" width=\"59\" height=\"53\" \/><br \/>\n<span style=\"text-decoration: underline;\">\u00a021.45<br \/>\n<\/span><br \/>\nExplanation:<span style=\"text-decoration: underline;\"><br \/>\n<\/span>1.95 &#8212;&#8212;2 decimal places<span style=\"text-decoration: underline;\"><br \/>\nX 11<br \/>\n<\/span>\u00a0 195<span style=\"text-decoration: underline;\"><br \/>\n1950<br \/>\n21.45&#8212;&#8211; 2 decimal places<br \/>\n<\/span>Therefore, 1.95 X 11 = 21.45.<span style=\"text-decoration: underline;\"><br \/>\n<\/span><\/p>\n<p>Question 22.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27323\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-254.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 254\" width=\"66\" height=\"54\" \/><br \/>\n<span style=\"text-decoration: underline;\">\u00a0 29.45<\/span><\/p>\n<p>Explanation:<br \/>\n4,4<br \/>\n5.89 &#8212;&#8212;2 decimal places<span style=\"text-decoration: underline;\"><br \/>\nX 5<br \/>\n<\/span><span style=\"text-decoration: underline;\">29.45&#8212;&#8211; 2 decimal places<br \/>\n<\/span>Therefore, 5.89 X 5 = 29.45.<\/p>\n<p>Question 23.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27324\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-255.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 255\" width=\"72\" height=\"61\" \/><br \/>\n<span style=\"text-decoration: underline;\">\u00a0 13.888<\/span><\/p>\n<p>Explanation:<span style=\"text-decoration: underline;\"><br \/>\n1,2<br \/>\n<\/span>3.472 &#8212;&#8212;3 decimal places<span style=\"text-decoration: underline;\"><br \/>\nX\u00a0 \u00a04<br \/>\n13.888&#8212;&#8211; 3 decimal places<br \/>\n<\/span>Therefore, 3.472 X 4 = 13.888.<span style=\"text-decoration: underline;\"><br \/>\n<\/span><\/p>\n<p>Question 24.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27325\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-256.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 256\" width=\"78\" height=\"57\" \/><br \/>\n<span style=\"text-decoration: underline;\">\u00a0 98.256<\/span><\/p>\n<p>Explanation:<span style=\"text-decoration: underline;\"><br \/>\n1,1<br \/>\n<\/span>8.188 &#8212;&#8212;3 decimal places<span style=\"text-decoration: underline;\"><br \/>\nX\u00a0 12<br \/>\n<\/span>16376<br \/>\n<span style=\"text-decoration: underline;\">81880<br \/>\n98.256&#8212;&#8211; 3 decimal places<br \/>\n<\/span>Therefore, 8.188 X 12 = 98.256.<span style=\"text-decoration: underline;\"><br \/>\n<\/span><\/p>\n<p>Question 25.<br \/>\n100 \u00d7 0.024<br \/>\n100 \u00d7 0.024 = 2.4<\/p>\n<p>Explanation:<br \/>\n0.024 &#8212; 3 decimal places<br \/>\n<span style=\"text-decoration: underline;\">X100<\/span><br \/>\n0000<br \/>\n00000<br \/>\n<span style=\"text-decoration: underline;\">002400<br \/>\n002.400&#8212;&#8211;3 decimal places<br \/>\n<\/span>Therefore, 0.02 X 100 = 2.4.<\/p>\n<p>Question 26.<br \/>\n19 \u00d7 0.004<br \/>\n19 \u00d7 0.004 = 0.076<\/p>\n<p>Explanation:<br \/>\n0.004 &#8212; 3 decimal places<br \/>\n<span style=\"text-decoration: underline;\">X19\u00a0 \u00a0<\/span><br \/>\n0036<br \/>\n<span style=\"text-decoration: underline;\">00040<br \/>\n0.076&#8212;&#8211;3 decimal places<br \/>\n<\/span>Therefore, 0.004 X 19 = 0.076.<\/p>\n<p>Question 27.<br \/>\n3.27 \u00d7 14<br \/>\n3.27 \u00d7 14 = 45.78<\/p>\n<p>Explanation:<br \/>\n8<br \/>\n3.27&#8212;&#8211; 2 decimal places<br \/>\n<span style=\"text-decoration: underline;\">X 14<br \/>\n<\/span>1308<br \/>\n<span style=\"text-decoration: underline;\">3270<br \/>\n45.78&#8212;- 2 decimal places<br \/>\n<\/span>Therefore, 3.27 X 14 = 45.78.<\/p>\n<p>Question 28.<br \/>\n46 . 5.448<br \/>\n46 X 5.448 = 250.608<\/p>\n<p>Explanation:<br \/>\n<span style=\"text-decoration: underline;\">\u00a01,1,3<\/span><br \/>\n<span style=\"text-decoration: underline;\">2, 2,4<\/span><br \/>\n5.448 &#8212;&#8211; 3 decimal places<br \/>\n<span style=\"text-decoration: underline;\">X 46<br \/>\n<\/span>\u00a0 32688<span style=\"text-decoration: underline;\"><br \/>\n217920<br \/>\n250.608 &#8212;-3 decimal places<br \/>\n<\/span>Therefore, 46 X 5.448 = 250.608.<\/p>\n<p>Question 29.<br \/>\n50 \u00d7 12.21<br \/>\n50 X 12.21 = 610.5<\/p>\n<p>Explanation:<br \/>\n1,1<br \/>\n12.21&#8212;-2 decimal places<br \/>\n<span style=\"text-decoration: underline;\">X 50<br \/>\n<\/span>\u00a00000<br \/>\n<span style=\"text-decoration: underline;\">6105<br \/>\n610.50&#8212;-2 decimal places<br \/>\n<\/span>Therefore 50 X 12.21 = 610.5.<\/p>\n<p>Question 30.<br \/>\n104 . 4.786<br \/>\n104 X 4.786 =497.744<\/p>\n<p>Explanation:<br \/>\n3,3,2<br \/>\n4.786&#8212;-3 decimal places<br \/>\n<span style=\"text-decoration: underline;\">X104<br \/>\n<\/span>019144<br \/>\n00000<br \/>\n<span style=\"text-decoration: underline;\">478600<br \/>\n497.744&#8212;-3 decimal places<br \/>\n<\/span>Therefore 104 X 4.786 = 497.744.<\/p>\n<p>Question 31.<br \/>\n0.0038 \u00d7 9<br \/>\n0.0038 X 9 = 0.0342<\/p>\n<p>Explanation:<br \/>\n3<br \/>\n0.0038&#8212;-4 decimal places<br \/>\n<span style=\"text-decoration: underline;\">X\u00a0 \u00a0 \u00a0 \u00a09<br \/>\n<\/span><span style=\"text-decoration: underline;\">0.0342&#8212;-4 decimal places<br \/>\n<\/span>Therefore, 0.0038 X 9 = 0.0342<\/p>\n<p>Question 32.<br \/>\n10 \u00d7 0.0093<br \/>\n10 \u00d7 0.0093 = 0.093<\/p>\n<p>Explanation:<br \/>\n3<br \/>\n0.0093&#8212;-4 decimal places<br \/>\n<span style=\"text-decoration: underline;\">X\u00a0 \u00a0 \u00a010<br \/>\n<\/span>\u00a0 00000<br \/>\n<span style=\"text-decoration: underline;\">000930<br \/>\n<\/span><span style=\"text-decoration: underline;\">0.0930 &#8212;-4 decimal places<br \/>\n<\/span>Therefore, 10 \u00d7 0.0093 = 0.093.<\/p>\n<p><strong>YOU BE THE TEACHER<\/strong><br \/>\n<strong>Your friend \ufb01nds the product. Is your friend correct? Explain your reasoning.<\/strong><\/p>\n<p>Question 33.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27326\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-257.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 257\" width=\"132\" height=\"120\" \/><br \/>\nYes, Friend is correct as 0.0045 X 9 = 0.0405,<\/p>\n<p>Explanation:<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 4,\u00a0 \u00a0<\/span><br \/>\n0.0045&#8212;&#8211; 4 decimal places<br \/>\n<span style=\"text-decoration: underline;\">X\u00a0 \u00a0 \u00a0 \u00a09<br \/>\n0.0405&#8212;&#8211;4 decimal places<br \/>\n<\/span>Therefore friend is correct as 0.0405 is equal to friends value 0.0405.<span style=\"text-decoration: underline;\"><br \/>\n<\/span>Question 34.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27327\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-258.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 258\" width=\"129\" height=\"130\" \/><br \/>\nNo, Friend is incorrect as 0.32 X 5 = 1.6 \u2260 0.160<\/p>\n<p>Explanation:<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 1\u00a0 \u00a0<\/span><br \/>\n0.32&#8212;&#8211;2 decimal places<br \/>\n<span style=\"text-decoration: underline;\">X\u00a0 \u00a05<br \/>\n1.60\u00a0 &#8212;-2 decimal places<br \/>\n<\/span>Therefore, friend is incorrect as 0.32 X 5 = 1.6 \u2260 0.160.<\/p>\n<p>Question 35.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nThe weight of an object on the Moon is about 0.167 of its weight on Earth.<br \/>\nHow much does a 180-pound astronaut weigh on the Moon?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27328\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-259.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 259\" width=\"180\" height=\"301\" \/><br \/>\nI80-pound astronaut weigh on the Moon is 30.06 pounds<\/p>\n<p>Explanation:<br \/>\nGiven the weight of an object on the Moon is about 0.167<br \/>\nof its weight on Earth. So, 180-pound astronaut weigh on the Moon is<br \/>\n0.167 X 180 = 30.06 pounds<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a05,5\u00a0 \u00a0<\/span><br \/>\n0.167 &#8212;&#8211; 3 decimal places<br \/>\n<span style=\"text-decoration: underline;\">X 180\u00a0\u00a0<\/span><br \/>\n0000<br \/>\n13360<br \/>\n<span style=\"text-decoration: underline;\">016700<br \/>\n30.060&#8212;- 3 decimal places<br \/>\n<\/span>Therefore, I80-pound astronaut weigh on the Moon is 30.06 pounds.<\/p>\n<p><strong>MULTIPLYING DECIMALS<\/strong><br \/>\n<strong>Multiply.<\/strong><\/p>\n<p>Question 36.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27329\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-260.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 260\" width=\"60\" height=\"54\" \/><br \/>\n<span style=\"text-decoration: underline;\">\u00a0 0.14<br \/>\n<\/span><br \/>\nExplanation:<br \/>\n1<br \/>\n0.7 &#8212;&#8212;1 decimal place<span style=\"text-decoration: underline;\"><br \/>\nX 0.2&#8212;&#8212;1 decimal place<br \/>\n<\/span>\u00a0 \u00a014<span style=\"text-decoration: underline;\"><br \/>\n000<br \/>\n0.14&#8212;&#8211; 2 decimal places<br \/>\n<\/span>Therefore, 0.7 X 0.2 = 0.14.<\/p>\n<p>Question 37.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27330\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-261.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 261\" width=\"65\" height=\"53\" \/><br \/>\n<span style=\"text-decoration: underline;\">\u00a00.024<\/span><\/p>\n<p>Explanation:<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 2<br \/>\n<\/span>0.08 &#8212;&#8212;&#8211;2 decimal places<span style=\"text-decoration: underline;\"><br \/>\nX 0.3&#8212;&#8212;&#8211;1 decimal place<br \/>\n<\/span>0024<span style=\"text-decoration: underline;\"><br \/>\n0000<br \/>\n0.024&#8212;&#8212;&#8211;3 decimal places<br \/>\n<\/span>Therefore, 0.08 X 0.3 = 0.024.<\/p>\n<p>Question 38.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27331\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-262.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 262\" width=\"75\" height=\"68\" \/><br \/>\n<span style=\"text-decoration: underline;\">0.00021<\/span><\/p>\n<p>Explanation:<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a02<br \/>\n<\/span>0.007 &#8212;&#8212;&#8211;3 decimal places<span style=\"text-decoration: underline;\"><br \/>\nX 0.03&#8212;&#8212;&#8211;2 decimal places<br \/>\n<\/span>\u00a0 0021<span style=\"text-decoration: underline;\"><br \/>\n<\/span>00000<span style=\"text-decoration: underline;\"><br \/>\n000000<br \/>\n0.00021&#8212;&#8212;-5 decimal places<br \/>\n<\/span>Therefore, 0.007 X 0.03 = 0.00021.<\/p>\n<p>Question 39.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27332\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-263.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 263\" width=\"68\" height=\"58\" \/><br \/>\n<span style=\"text-decoration: underline;\">0.000072<\/span><\/p>\n<p>Explanation:<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a07<br \/>\n<\/span>0.0008 &#8212;&#8212;-4 decimal places<span style=\"text-decoration: underline;\"><br \/>\nX 0.09&#8212;&#8212;&#8211;2 decimal places<br \/>\n<\/span>\u00a0 00072<br \/>\n000000<span style=\"text-decoration: underline;\"><br \/>\n0000000<br \/>\n<\/span><span style=\"text-decoration: underline;\">0.000072&#8212;&#8211;6 decimal places<br \/>\n<\/span>Therefore, 0.0008 X 0.09 = 0.000072.<span style=\"text-decoration: underline;\"><br \/>\n<\/span><\/p>\n<p>Question 40.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27333\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-264.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 264\" width=\"60\" height=\"57\" \/><br \/>\n<span style=\"text-decoration: underline;\">0.0036<\/span><\/p>\n<p>Explanation:<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 3\u00a0 \u00a0<\/span><br \/>\n0.004 &#8212;&#8212;-3 decimal places<br \/>\n<span style=\"text-decoration: underline;\">X\u00a0 0.9&#8212;&#8212;-1 decimal place<br \/>\n<\/span>\u00a0 0036<br \/>\n<span style=\"text-decoration: underline;\">00000<\/span><br \/>\n<span style=\"text-decoration: underline;\">0.0036&#8212;&#8212;-4 decimal places<br \/>\n<\/span>Therefore, 0.004 X 0.9 = 0.0036.<\/p>\n<p>Question 41.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27334\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-265.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 265\" width=\"63\" height=\"61\" \/><br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a00.03<\/span><\/p>\n<p>Explanation:<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a03<\/span><br \/>\n0.06&#8212;&#8211;2\u00a0decimal places<br \/>\n<span style=\"text-decoration: underline;\">X 0.5&#8212;&#8211;1 decimal place<br \/>\n<\/span>0030<span style=\"text-decoration: underline;\"><br \/>\n0000<br \/>\n0.030&#8212;-3 decimal places<br \/>\n<\/span>Therefore, 0.06 X 0.5 = 0.03.<\/p>\n<p>Question 42.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27335\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-266.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 266\" width=\"81\" height=\"60\" \/><br \/>\n<span style=\"text-decoration: underline;\">0.0000032<\/span><\/p>\n<p>Explanation:<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 3<\/span><br \/>\n0.0008&#8212;&#8212;-4 decimal places<br \/>\n<span style=\"text-decoration: underline;\">X 0.004&#8212;&#8212;3 decimal places<br \/>\n<\/span>\u00a0 \u00a000032<br \/>\n000000<br \/>\n<span style=\"text-decoration: underline;\">0000000<br \/>\n<\/span><span style=\"text-decoration: underline;\">0.0000032&#8212;-7 decimal places<br \/>\n<\/span>Therefore, 0.0008 X 0.004 = 0.0000032.<\/p>\n<p>Question 43.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27336\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-267.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 267\" width=\"73\" height=\"57\" \/><br \/>\n<span style=\"text-decoration: underline;\">0.000012<\/span><\/p>\n<p>Explanation:<br \/>\n1<br \/>\n0.0002&#8212;&#8212;-4 decimal places<span style=\"text-decoration: underline;\"><br \/>\nX 0.06&#8212;&#8212;\u00a0 2 decimal places<br \/>\n00012<br \/>\n000000<br \/>\n0000000<br \/>\n0.000012&#8212;-6 decimal places<br \/>\n<\/span>Therefore, 0.0002 X 0.06 = 0.000012.<span style=\"text-decoration: underline;\"><br \/>\n<\/span><\/p>\n<p>Question 44.<br \/>\n12.4 \u00d7 0.2<br \/>\n12.4 X 0.2 = 2.48<\/p>\n<p>Explanation:<br \/>\n12.4&#8212;&#8212;&#8211;1 decimal place<br \/>\n<span style=\"text-decoration: underline;\">X 0.2&#8212;&#8212;-1 decimal place<\/span><br \/>\n248<br \/>\n<span style=\"text-decoration: underline;\">0000<br \/>\n2.48&#8212;&#8212;-2 decimal places<br \/>\n<\/span>Therefore, 12.4\u00a0 X 0.2 = 2.48.<\/p>\n<p>Question 45.<br \/>\n18.6 . 5.9<br \/>\n18.6 X 5.9 = 109.74<\/p>\n<p>Explanation:<br \/>\n<span style=\"text-decoration: underline;\">\u00a04,3<\/span><br \/>\n<span style=\"text-decoration: underline;\">7,5<\/span><br \/>\n18.6&#8212;-<span style=\"text-decoration: underline;\">1 decimal place<\/span><br \/>\n<span style=\"text-decoration: underline;\">X5.9&#8212; 1 decimal place<br \/>\n<\/span>1674<span style=\"text-decoration: underline;\"><br \/>\n9300<br \/>\n109.74&#8212;-2 decimal places<br \/>\n<\/span>Therefore, 18.6 X 5.9 = 109.74.<\/p>\n<p>Question 46.<br \/>\n7.91 \u00d7 0.72<br \/>\n7.91 X 0.72 = 5.6952<\/p>\n<p>Explanation:<br \/>\n<span style=\"text-decoration: underline;\">\u00a06<\/span><br \/>\n<span style=\"text-decoration: underline;\">\u00a01<\/span><br \/>\n7.91&#8212;&#8211;2 decimal places<br \/>\n<span style=\"text-decoration: underline;\">X0.72&#8212;-2 decimal places<br \/>\n<\/span>01582<br \/>\n55370<br \/>\n<span style=\"text-decoration: underline;\">00000<br \/>\n5.6952&#8212;-4 decimal places<br \/>\n<\/span>Therefore, 7.91 X 0.72 = 5.6952.<\/p>\n<p>Question 47.<br \/>\n1.16 \u00d7 3.35<br \/>\n1.16 \u00d7 3.35 = 3.886<\/p>\n<p>Explanation:<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a01\u00a0\u00a0<\/span><br \/>\n<span style=\"text-decoration: underline;\">\u00a0\u00a0 1\u00a0\u00a0<\/span><br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 3<\/span><br \/>\n1.16&#8212;&#8212;-2 decimal places<br \/>\n<span style=\"text-decoration: underline;\">X 3.35&#8212;&#8211;2 decimal places<br \/>\n<\/span>00580<br \/>\n03480<br \/>\n<span style=\"text-decoration: underline;\">34800<\/span><br \/>\n<span style=\"text-decoration: underline;\">3.8860&#8212;&#8211;4 decimal places<br \/>\n<\/span>Therefore, 1.16 X 3.35 = 3.8860.<\/p>\n<p>Question 48.<br \/>\n6.478 \u00d7 18.21<br \/>\n6.478 \u00d7 18.21 = 117.96438<\/p>\n<p>Explanation:<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 3,5,6\u00a0<\/span><br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a01,1<\/span><br \/>\n6.478&#8212;&#8212;3\u00a0decimal places<br \/>\n<span style=\"text-decoration: underline;\">X 18.21&#8212;-2 decimal places<br \/>\n<\/span>0006478<br \/>\n0129560<br \/>\n5182400<br \/>\n<span style=\"text-decoration: underline;\">6478000<br \/>\n117.96438&#8212;5\u00a0decimal places<br \/>\n<\/span>Therefore, 6.478 \u00d7 18.21 = 117.96438.<\/p>\n<p>Question 49.<br \/>\n1.9 \u00d7 7.216<br \/>\n1.9 X 7.216 = 13.7104<\/p>\n<p>Explanation:<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a01,1,5<\/span><br \/>\n7.216&#8212;&#8212;3\u00a0decimal places<br \/>\n<span style=\"text-decoration: underline;\">X 1.9&#8212;&#8212;1 decimal place<br \/>\n<\/span>\u00a064944<br \/>\n<span style=\"text-decoration: underline;\">\u00a072160<\/span><br \/>\n<span style=\"text-decoration: underline;\">13.7104&#8212;&#8212;4 decimal places<br \/>\n<\/span>Therefore, 7.216 X 1.9 = 13.7104.<\/p>\n<p>Question 50.<br \/>\n0.0021 \u00d7 18.2<br \/>\n0.0021 \u00d7 18.2 = 0.03822<\/p>\n<p>Explanation:<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 1\u00a0\u00a0<\/span><br \/>\n0.0021&#8212;&#8212;3\u00a0decimal places<br \/>\n<span style=\"text-decoration: underline;\">X 18.2&#8212;&#8212;-1 decimal place<\/span><br \/>\n0000042<br \/>\n0001680<br \/>\n<span style=\"text-decoration: underline;\">0002100<br \/>\n0.03822&#8212;&#8212;4 decimal places<br \/>\n<\/span>Therefore, 0.0021 X 18.2 = 0.03822.<\/p>\n<p>Question 51.<br \/>\n6.109 . 8.4<br \/>\n6.109 X 8.4 = 51.3156<\/p>\n<p>Explanation:<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a07\u00a0 \u00a0<\/span><br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a03\u00a0 \u00a0<\/span><br \/>\n6.109&#8212;&#8212;3\u00a0decimal places<br \/>\n<span style=\"text-decoration: underline;\">X 8.4&#8212;&#8212;1 decimal place<br \/>\n<\/span>024436<span style=\"text-decoration: underline;\"><br \/>\n488720<br \/>\n51.3156&#8212;&#8212;4 decimal places<br \/>\n<\/span>Therefore, 6.109 X 8.4 = 51.3156.<\/p>\n<p>Question 52.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend \ufb01nds the product of 4.9 and 3.8. Is your friend correct? Explain your reasoning.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27337\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-268.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 268\" width=\"128\" height=\"108\" \/><br \/>\nNo, Friend is incorrect as 4.9 X 3.8 = 18.62 \u2260 186.2<\/p>\n<p>Explanation:<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a02<\/span><br \/>\n<span style=\"text-decoration: underline;\">\u00a0 7<\/span><br \/>\n4.9 &#8212;&#8212;1 decimal place<br \/>\n<span style=\"text-decoration: underline;\">X3.8&#8212;&#8212;1 decimal place<br \/>\n<\/span>0392<span style=\"text-decoration: underline;\"><br \/>\n1470<br \/>\n18.62&#8212;&#8212;2 decimal places<br \/>\n<\/span>Therefore, Friend is incorrect as\u00a04.9 X 3.8 = 18.62 \u2260 186.2.<\/p>\n<p>Questi1on 53.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nA Chinese restaurant offers buffet takeout for $4.99 per pound.<br \/>\nHow much does your takeout meal cost?<br \/>\nThe takeout meal cost $3.5429<\/p>\n<p>Explanation:<br \/>\nGiven a Chinese restaurant offers buffet takeout for $4.99 per pound<br \/>\nand 1 dollar in pound = 0.71 pound, So the takeout meal costs<br \/>\n$4.99 X 0.71 = $3.5429<br \/>\n4.99&#8212;&#8212;2 decimal places<br \/>\n<span style=\"text-decoration: underline;\">X0.71&#8212;&#8212;2 decimal places<br \/>\n<\/span>00499<br \/>\n34930<br \/>\n<span style=\"text-decoration: underline;\">00000<br \/>\n3.5429&#8212;&#8212;4 decimal places<br \/>\n<\/span>Therefore, the takeout meal cost $3.5429.<\/p>\n<p>Question 54.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nOn a tour of an old gold mine, you \ufb01nd a nugget containing<br \/>\n0.82 ounce of gold. Gold is worth $1323.80 per ounce.<br \/>\nHow much is your nugget worth?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27338\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-269.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 269\" width=\"212\" height=\"251\" \/><br \/>\nThe nugget worth is $1085.516,<\/p>\n<p>Explanation:<br \/>\nGiven I found a nugget containing 0.82 ounce of gold.<br \/>\nand gold is worth $1323.80 per ounce. So my nugget worth is<br \/>\n$1323.80 X 0.82<br \/>\n<span style=\"text-decoration: underline;\">2,1,2,6<\/span><br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a01\u00a0<\/span><br \/>\n1323.80&#8212;&#8211;2 decimal places<br \/>\n<span style=\"text-decoration: underline;\">X 0.82&#8212;&#8212;-2 decimal places<br \/>\n<\/span>00264760<br \/>\n10590400<span style=\"text-decoration: underline;\"><br \/>\n00000000<br \/>\n1085.5160&#8212;-4 decimal places<br \/>\n<\/span>Therefore, the nugget worth is $1085.516.<\/p>\n<p>Question 55.<br \/>\n<strong>PRECISION<\/strong><br \/>\nOne meter is approximately 3.28 feet. Find the height of each building in feet.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27339\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-270.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 270\" width=\"476\" height=\"228\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-270.png 476w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-270-300x144.png 300w\" sizes=\"(max-width: 476px) 100vw, 476px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27340\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-271.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 271\" width=\"164\" height=\"505\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-271.png 164w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-271-97x300.png 97w\" sizes=\"(max-width: 164px) 100vw, 164px\" \/><br \/>\nCarlton Centre is 731.44 feet,<br \/>\nBurj Khalifa is 2715.84 feet,<br \/>\nQ1 is 1059.44 feet,<br \/>\nFederation Tower is 1226.72 feet,<br \/>\nOne World Trade Centre is\u00a0 1774.48 feet,<br \/>\nGran Torre Santiago is 984 feet,<\/p>\n<p>Explanation:<br \/>\nGiven one meter is approximately 3.28 feet and<br \/>\nheightsof each building in meters in the table above,<br \/>\nnow we will find height in feet as<br \/>\na. Carlton Centre is 223 meters, So in feet it\u00a0 is<br \/>\n223 X 3.28 = 731.44<br \/>\n<span style=\"text-decoration: underline;\">\u00a01,2<\/span><br \/>\n223<br \/>\n<span style=\"text-decoration: underline;\">X3.28&#8212;&#8212;&#8212;&#8211;2 decimal places<br \/>\n<\/span>01784<br \/>\n04460<br \/>\n<span style=\"text-decoration: underline;\">66900<br \/>\n731.44&#8212;&#8212;-2 decimal places<br \/>\n<\/span>So, Carlton Centre is 731.44 feet,<br \/>\nb. Burj Khalifa is 828 meters , In feet is<br \/>\n828 X 3.28 = 2715.84<br \/>\n<span style=\"text-decoration: underline;\">2\u00a0 \u00a0 \u00a0 \u00a0\u00a0<\/span><br \/>\n<span style=\"text-decoration: underline;\">1,\u00a0 \u00a0 \u00a0 \u00a0\u00a0<\/span><br \/>\n<span style=\"text-decoration: underline;\">1,6\u00a0 \u00a0<\/span><br \/>\n828<br \/>\n<span style=\"text-decoration: underline;\">X3.28 &#8212;&#8212;&#8211; 2 decimal places<br \/>\n<\/span>006624<br \/>\n016560<br \/>\n<span style=\"text-decoration: underline;\">248400<br \/>\n2715.84&#8212;&#8212;-2 decimal places<br \/>\n<\/span>So, Burj Khalifa is 2715.84 feet,<br \/>\nc. Q1 is 323 meters, In feet is<br \/>\n323 X 3.28 = 1059.44<br \/>\n<span style=\"text-decoration: underline;\">1,2<\/span><br \/>\n323<br \/>\n<span style=\"text-decoration: underline;\">X3.28&#8212;&#8212;-2 decimal places<br \/>\n<\/span>02584<br \/>\n06460<br \/>\n<span style=\"text-decoration: underline;\">96900<\/span><br \/>\n<span style=\"text-decoration: underline;\">1059.44&#8212;&#8212;-2 decimal places<br \/>\n<\/span>So, Q1 is 1059.44 feet,<br \/>\nd. Federation Tower is 374 meters, In feet is<br \/>\n374 X 3.28 = 1226.72<br \/>\n<span style=\"text-decoration: underline;\">\u00a05,3<\/span><br \/>\n374<br \/>\n<span style=\"text-decoration: underline;\">X 3.28&#8212;&#8212;-2 decimal places<br \/>\n<\/span>002992<br \/>\n007480<br \/>\n<span style=\"text-decoration: underline;\">112200<br \/>\n1226.72&#8212;&#8212;-2 decimal places<br \/>\n<\/span>So, Federation Tower is 1226.72 feet,<br \/>\ne. One World Trade Centre is 541 meters, In feet is<br \/>\n541 X 3.28 = 1774.48<br \/>\n<span style=\"text-decoration: underline;\">1<\/span><br \/>\n<span style=\"text-decoration: underline;\">\u00a03<\/span><br \/>\n541<br \/>\n<span style=\"text-decoration: underline;\">X3.28&#8212;&#8212;-2 decimal places<br \/>\n<\/span>004328<br \/>\n010820<br \/>\n<span style=\"text-decoration: underline;\">162300<br \/>\n1774.48&#8212;&#8212;-2 decimal places<br \/>\n<\/span>So, One World Trade Centre is\u00a0 1774.48 feet,<br \/>\nf. Gran Torre Santiago is 300 meters, Now in feet is<br \/>\n300 X 3.28 = 984<span style=\"text-decoration: underline;\"><br \/>\n<\/span>300<span style=\"text-decoration: underline;\"><br \/>\nX 3.28&#8212;&#8212;-2 decimal places<br \/>\n<\/span>02400<br \/>\n06000<br \/>\n<span style=\"text-decoration: underline;\">90000<\/span><br \/>\n<span style=\"text-decoration: underline;\">984.00&#8212;&#8212;-2 decimal places<br \/>\n<\/span>So, Gran Torre Santiago is 984 feet.<\/p>\n<p>Question 56.<br \/>\n<strong>REASONING<\/strong><br \/>\nShow how to evaluate (7.12 \u00d7 8.22) \u00d7 100 without multiplying two decimals.<br \/>\n(7.12 X 8.22) X 100 = 5852.64<\/p>\n<p>Explanation:<br \/>\nFirst multiply as whole numbers only we get 712 X 822 = 585264,<br \/>\nWe have 4 decimal places but it is multiplied by 100,<br \/>\nWe get 2 decimal places so we put as 5852.64,<br \/>\nTherefore (7.12 \u00d7 8.22) \u00d7 100 = 5852.64.<\/p>\n<p><strong>EVALUATING AN EXPRESSION<\/strong><\/p>\n<p><strong>Evaluate the expression.<\/strong><\/p>\n<p>Question 57.<br \/>\n2.4 \u00d7 16 + 7<br \/>\n2.4 \u00d7 16 + 7 = 45.4<\/p>\n<p>Explanation:<br \/>\nGiven expression as 2.4 \u00d7 16 + 7, So first we calculate<br \/>\n2.4 X 16 as<br \/>\n<span style=\"text-decoration: underline;\">\u00a02<br \/>\n<\/span>2.4&#8212;&#8212;1 decimal place<br \/>\n<span style=\"text-decoration: underline;\">x16<\/span><br \/>\n144<br \/>\n<span style=\"text-decoration: underline;\">240<br \/>\n38.4&#8212;- 1 decimal place<br \/>\n<\/span>Now 38.4 + 7 = 45.4<br \/>\nTherefore, 2.4 \u00d7 16 + 7 = 45.4<\/p>\n<p>Question 58.<br \/>\n6.85 \u00d7 2 \u00d7 10<br \/>\n6.85 \u00d7 2 \u00d7 10 = 137<\/p>\n<p>Explanation:<br \/>\nGiven expression as 6.85 \u00d7 2 \u00d7 10,<br \/>\nFirst we calculate 6.85 X 2 as<br \/>\n1,1<br \/>\n6.85&#8212;&#8211;2 decimal places<br \/>\n<span style=\"text-decoration: underline;\">X 2<br \/>\n13.70&#8212;&#8211;2 decimal places<br \/>\n<\/span>Now, 13.70 X 10 we move 1 decimal place as 137.0,<br \/>\nTherefore 6.85 \u00d7 2 \u00d7 10 = 137.<\/p>\n<p>Question 59.<br \/>\n1.047 \u00d7 5 &#8211; 0.88<br \/>\n1.047 \u00d7 5 &#8211; 0.88 = 4.355<\/p>\n<p>Explanation:<br \/>\nGiven expression as 1.047 \u00d7 5 &#8211; 0.88, First we calculate<br \/>\n1.047 X 5 as<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 2,3<\/span><br \/>\n1.047&#8212; 3 decimal places<br \/>\n<span style=\"text-decoration: underline;\">X\u00a0 \u00a05<br \/>\n5.235&#8212; 3 decimal places<\/span><br \/>\nNow 5.235 &#8211; 0.88<br \/>\n5.235<br \/>\n<span style=\"text-decoration: underline;\">0.880<br \/>\n4.355<br \/>\n<\/span>Therefore, 1.047 \u00d7 5 &#8211; 0.88 = 4.355.<\/p>\n<p>Question 60.<br \/>\n4.32(3.7 + 1.65)<br \/>\n4.32 X (3.7 + 1.65) = 23.112<\/p>\n<p>Explanation:<br \/>\nGiven expression as 4.32(3.7 + 1.65), first we calculate<br \/>\n(3.7 + 1.65) = 5.35<br \/>\n3.70<br \/>\n<span style=\"text-decoration: underline;\">+1.65<br \/>\n5.35<br \/>\n<\/span>Now, we multiply as 4.32 X 5.35 as<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 1,1<\/span><br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a01,1<br \/>\n<\/span>4.32 &#8212;&#8212;2 decimal places<span style=\"text-decoration: underline;\"><br \/>\nX5.35&#8212;&#8211;2 decimal places<br \/>\n<\/span>02160<br \/>\n12960<span style=\"text-decoration: underline;\"><br \/>\n21600<br \/>\n23.1120&#8212;&#8211;4 decimal places<br \/>\n<\/span>Therefore, 4.32 X (3.7 + 1.65) = 23.112<\/p>\n<p>Question 61.<br \/>\n23.98 &#8211; 1.7<sup>2<\/sup> . 7.6<br \/>\n23.98 &#8211; 1.7<sup>2<\/sup> . 7.6 = 2.016<\/p>\n<p>Explanation:<br \/>\nGiven expression as 23.98 &#8211; 1.7<sup>2<\/sup> . 7.6, first we calculate<br \/>\n(1.7<sup>2<\/sup> X 7.6) = (1.7 X 1.7 X 7.6) again here first we<br \/>\nmultiply 1.7 X 1.7 as<br \/>\n<span style=\"text-decoration: underline;\">4\u00a0 \u00a0\u00a0<\/span><br \/>\n1.7&#8212;&#8212; 1 decimal place<br \/>\n<span style=\"text-decoration: underline;\">X1.7&#8212;&#8211; 1 decimal place<\/span><br \/>\n119<br \/>\n<span style=\"text-decoration: underline;\">170<br \/>\n2.89&#8212;&#8211; 2 decimal places<br \/>\n<\/span>Now we multiply with 2.89 with 7.6 as<br \/>\n<span style=\"text-decoration: underline;\">6,6<\/span><br \/>\n<span style=\"text-decoration: underline;\">\u00a0 5,5<\/span><br \/>\n2.89&#8212;&#8212; 2 decimal places<br \/>\n<span style=\"text-decoration: underline;\">X7.6&#8212;&#8212; 1 decimal place<br \/>\n<\/span>01734<br \/>\n<span style=\"text-decoration: underline;\">20230<\/span><br \/>\n<span style=\"text-decoration: underline;\">21.964&#8212;-3 decimal places<br \/>\n<\/span>Now further we find 23.98 minus 21.964 as<br \/>\n23.980<br \/>\n<span style=\"text-decoration: underline;\">-21.964<br \/>\n2.016<\/span><br \/>\nTherefore 23.98 &#8211; 1.7<sup>2<\/sup> . 7.6 = 2.016.<\/p>\n<p>Question 62.<br \/>\n12 . 5.16 + 10.064<br \/>\n12 . 5.16 + 10.064 = 182.688<\/p>\n<p>Explanation:<br \/>\nGiven expression as 12 X (5.16 + 10.064), first we calculate<br \/>\n5.16 + 10.064 as<\/p>\n<p>05.160<br \/>\n<span style=\"text-decoration: underline;\">+10.064<\/span><br \/>\n<span style=\"text-decoration: underline;\">15.224<br \/>\n<\/span>Now we calculate 12 X 15.224 as<br \/>\n<span style=\"text-decoration: underline;\">1<br \/>\n<\/span>15.224&#8212;&#8212;&#8212;3 decimal places<span style=\"text-decoration: underline;\"><br \/>\nX\u00a0 \u00a0 12<br \/>\n<\/span>030448<span style=\"text-decoration: underline;\"><br \/>\n152240<br \/>\n182.688&#8212;&#8212;&#8212;3 decimal places<br \/>\n<\/span>Therefore 12 . 5.16 + 10.064 = 182.688.<\/p>\n<p>Question 63.<br \/>\n0.9(8.2 . 20.35)<br \/>\n0.9(8.2 . 20.35) = 150.183<\/p>\n<p>Explanation:<br \/>\nGiven expression as 0.9(8.2 . 20.35), First we calculate<br \/>\n8.2 X 20.35 as<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 2,4\u00a0\u00a0<\/span><br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a01\u00a0\u00a0<\/span><br \/>\n20.35&#8212;&#8211; 2 decimal places<br \/>\n<span style=\"text-decoration: underline;\">X8.2 &#8212;&#8212;1 decimal place<\/span><br \/>\n004070<br \/>\n<span style=\"text-decoration: underline;\">162800<br \/>\n166.870&#8212;&#8211;3 decimal places<br \/>\n<\/span>Now we multiply 0.9 with 166.870 as<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a06, 6,7,6<br \/>\n<\/span>166.870&#8212;&#8211;3 decimal places<br \/>\n<span style=\"text-decoration: underline;\">X\u00a0 \u00a0 \u00a0 0.9&#8212;&#8211;1 decimal place<br \/>\n150.183&#8212;&#8211;3 decimal places<br \/>\n<\/span>Therefore 0.9(8.2 . 20.35) = 150.183.<\/p>\n<p>Question 64.<br \/>\n7.5<sup>2<\/sup>(6.084 &#8211; 5.44)<br \/>\n7.5<sup>2<\/sup>(6.084 &#8211; 5.44) = 36.225<\/p>\n<p>Explanation:<br \/>\nGiven expression as 7.5<sup>2<\/sup>(6.084 &#8211; 5.44), First we will find<br \/>\n6.084 &#8211; 5.44 as<br \/>\n6.084<br \/>\n<span style=\"text-decoration: underline;\">-5.440<\/span><br \/>\n<span style=\"text-decoration: underline;\">0.644<br \/>\n<\/span>Now 7.5<sup>2 <\/sup>X 0.644 as (7.5 X 7.5 X 0.644) as<br \/>\n<span style=\"text-decoration: underline;\">3<\/span><br \/>\n<span style=\"text-decoration: underline;\">\u00a0 2<\/span><br \/>\n7.5&#8212;&#8211;1 decimal place<br \/>\n<span style=\"text-decoration: underline;\">X7.5&#8212;-1 decimal place<\/span><br \/>\n0375<br \/>\n<span style=\"text-decoration: underline;\">5250<br \/>\n56.25&#8212;2 decimal places<br \/>\n<\/span>Now 56.25 X 0.644 as<br \/>\n56.25&#8212;&#8211;2 decimal places<br \/>\n<span style=\"text-decoration: underline;\">X0.644&#8212;&#8211;3 decimal places<\/span><br \/>\n00022500<br \/>\n00225000<br \/>\n03375000<br \/>\n<span style=\"text-decoration: underline;\">00000000<br \/>\n36.22500&#8212;-5 decimal places<br \/>\n<\/span>Therefore 7.5<sup>2<\/sup>(6.084 &#8211; 5.44) = 36.225.<\/p>\n<p>Question 65.<br \/>\n0.629[81 \u00f7 (10 \u00d7 2.7)]<br \/>\n0.629[81 \u00f7 (10 \u00d7 2.7)] = 1.887<\/p>\n<p>Explanation:<br \/>\nGiven expression as 0.629[81 \u00f7 (10 \u00d7 2.7)], First we will find<br \/>\n10 X 2.7 = 27.0 1 decimal place = 27,<br \/>\nNow 81 \u00f7\u00a0 27 = 3(as 27 X 3 = 81), Now<br \/>\n0.629 X 3 is<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a02 \u00a0 \u00a0<\/span><br \/>\n0.629&#8212;- 3 decimal places<br \/>\n<span style=\"text-decoration: underline;\">X\u00a0 \u00a0 3<br \/>\n1.887&#8212;- 3 decimal places<br \/>\n<\/span>So, 0.629[81 \u00f7 (10 \u00d7 2.7)] = 1.887<\/p>\n<p>Question 66.<br \/>\n<strong>REASONING<\/strong><br \/>\nWithout multiplying, how many decimal places does 3.4<sup>2<\/sup> have? 3.43<sup>3<\/sup>? 3.4<sup>4<\/sup>? Explain your reasoning.<br \/>\n3.4<sup>2<\/sup> will have 2 decimal places<br \/>\n3.43<sup>3 <\/sup>will have 6 decimal places<br \/>\n3.4<sup>4<\/sup>\u00a0will have 4 decimal places<\/p>\n<p>Explanation:<br \/>\nWe have 3.4<sup>2<\/sup> ,3.43<sup>3<\/sup>,3.4<sup>4 <\/sup>without multiplying we write<br \/>\ndecimal places as 3.4<sup>2<\/sup> will have 2 decimal places<br \/>\n3.43<sup>3 <\/sup>will have 6 decimal places<br \/>\n3.4<sup>4<\/sup> will have 4 decimal places,<br \/>\nWe take as 3.4<sup>2<\/sup> , 1 +1 decimal places = 2 decimal places,<br \/>\n3.43<sup>3<\/sup> , 2 decimals X 3 = 6 decimal places and<br \/>\n3.4<sup>4<\/sup> , 1 decimal X 4 = 4 decimal places and so on like<br \/>\nnumber of decimal places multiplied by powers.<\/p>\n<p>Question 67.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nYou buy 2.6 pounds of apples and 1.475 pounds of peaches. You hand the cashier a $20 bill. How much change will you receive?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27341\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-272.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 272\" width=\"259\" height=\"186\" \/><br \/>\nI will receive a change of $14.03,<\/p>\n<p>Explanation:<br \/>\nGiven 2.6 pounds of apples and 1.475 pounds of peaches I buyed,<br \/>\nApples are $1.23 per pound means the cost of apples<br \/>\nbought are 1.23 X 2.6 =3.198<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 1,1<\/span><br \/>\n1.23&#8212;&#8211;2 decimal places<br \/>\n<span style=\"text-decoration: underline;\">X2.6&#8212;&#8211;1 decimal place<br \/>\n<\/span>0738<br \/>\n<span style=\"text-decoration: underline;\">2460<br \/>\n3.198&#8212;&#8211;3 decimal places<br \/>\n<\/span>Now as cost of peaches are $1.88 per pound<br \/>\ntotal cost of peaches are 1.475 X 1.88 = 2.77300<br \/>\n<span style=\"text-decoration: underline;\">3,6,4<\/span><br \/>\n<span style=\"text-decoration: underline;\">3,6,4<br \/>\n<\/span>1.475&#8212;&#8211;3 decimal places<span style=\"text-decoration: underline;\"><br \/>\nX1.88&#8212;&#8211;2 decimal places<br \/>\n<\/span>011800<br \/>\n118000<span style=\"text-decoration: underline;\"><br \/>\n147500<br \/>\n2.77300&#8212;&#8211;5 decimal places<br \/>\n<\/span>So, Total cost for apples and peaches are 3.198 plus 2.77300<br \/>\n3.198<br \/>\n<span style=\"text-decoration: underline;\">+2.773<br \/>\n5.971<br \/>\n<\/span>We got total cost for fruits as $5.971, I hand<br \/>\nthe cashier $20, I will receive a change of 20-5.971 = 14.029<span style=\"text-decoration: underline;\"><br \/>\n<\/span>20.000<span style=\"text-decoration: underline;\"><br \/>\n-05.971<br \/>\n14.029<br \/>\n<\/span>Therefore I will receive a change of $14.029 \u2248$14.03 in return.<\/p>\n<p><strong>PATTERNS<\/strong><br \/>\n<strong>Describe the pattern. Find the next three numbers.<\/strong><\/p>\n<p>Question 68.<br \/>\n1, 0.6, 0.36, 0.216, . . .<br \/>\n1, 0.6, 0.36, 0.216, 0.1296, 0.07776,0.046656<\/p>\n<p>Explanation:<br \/>\nGiven series as 1, 0.6, 0.36, 0.216, . . .<br \/>\neach number is multiplied by 0.6<br \/>\nbecause 0.6 X 0.6 = 0.36,<br \/>\n0.36 X 0.6 = 0.216,<br \/>\nNext number is 0.216 X 0.6 = 0.1296,<br \/>\nthe next number is 0.1296 X 0.6 = 0.07776 and<br \/>\nthe next number is 0.0776 X 0.6 = 0.046656 and so on,<br \/>\nTherefore 1, 0.6, 0.36, 0.216, . . . the next three numbers are<br \/>\n1, 0.6, 0.36, 0.216, 0.1296, 0.07776, 0.046656 .<\/p>\n<p>Question 69.<br \/>\n15, 1.5, 0.15, 0.015, . . .<br \/>\n15, 1.5, 0.15, 0.015, 0.0015, 0.00015, 0.000015<\/p>\n<p>Explanation:<br \/>\nGiven series as 15, 1.5, 0.15, 0.015, . . .<br \/>\neach number is multiplied by 0.1<br \/>\nbecause 15 X 0.1 = 1.5,<br \/>\n1.5 X 0.1 = 0.15,<br \/>\n0.15 X 0.1 = 0.015,<br \/>\nthe next number is 0.015 X 0.1 = 0.0015 and<br \/>\nthe next number is 0.0015 X 0.1 = 0.00015 and<br \/>\nthe next number is 0.00015 X 0.1 = 0.000015 so on,<br \/>\nTherefore 15, 1.5, 0.15, 0.015, . . . the next three numbers are<br \/>\n15, 1.5, 0.15, 0.015, 0.0015, 0.00015, 0.000015.<\/p>\n<p>Question 70.<br \/>\n0.04, 0.02, 0.01, 0.005, . . .<br \/>\n0.04, 0.02, 0.01, 0.005, 0.0025, 0.00125, 0.000625<\/p>\n<p>Explanation:<br \/>\nGiven series as 0.04, 0.02, 0.01, 0.005 each number is<br \/>\ndivided by 2 as 0.04 \u00f7 2 = 0.02,<br \/>\n0.02 \u00f7 2 = 0.01, 0.01 \u00f7 2 = 0.005,<br \/>\nthe next number is 0.005 \u00f7 2 = 0.0025,<br \/>\nthe next number is 0.0025 \u00f7 2 = 0.00125,<br \/>\nand the next number is 0.00125 \u00f7 2 = 0.000625<br \/>\nand so on, therefore 0.04, 0.02, 0.01, 0.005, . . .<br \/>\nthe next three numbers are<br \/>\n0.04, 0.02, 0.01, 0.005, 0.0025, 0.00125, 0.000625 respectively.<\/p>\n<p>Question 71.<br \/>\n5, 7.5, 11.25, 16.875, . . .<br \/>\n5, 7.5, 11.25, 16.875, 25.3125, 37.96875, 56.953125<\/p>\n<p>Explanation:<br \/>\nGiven series are 5, 7.5, 11.25, 16.875, each number<br \/>\nis multiplied by 1.5 of the previous number as shown, So<br \/>\n5 X 1.5 = 7.5, 7.5 X 1.5 = 11.25, 11.25 X 1.5 = 16.875,<br \/>\nthe next number is 16.875 X 1.5 = 25.3125,<br \/>\nthe next number after 25.3125 X 1.5 = 37.96875 and<br \/>\nthe next number is 37.96875 X 1.5 = 56.953125.<br \/>\ntherefore 5, 7.5, 11.25, 16.875, the next three numbers are<br \/>\n5, 7.5, 11.25, 16.875, 25.3125, 37.96875, 56.953125.<\/p>\n<p>Question 72.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nYou are preparing for a trip to Canada. At the time of your trip,<br \/>\neach U.S dollar is worth 1.293 Canadian dollars and each<br \/>\nCanadian dollar is worth 0.773 U.S dollar.<br \/>\na. You exchange 150 U.S dollars for Canadian dollars. How many<br \/>\nCanadian dollars do you receive?<br \/>\nb. You spend 120 Canadian dollars on the trip. Then you exchange<br \/>\nthe remaining Canadian dollars for U.S dollars.<br \/>\nHow many U.S dollars do you receive?<br \/>\na. I receive 193.95 Canadian dollars,<br \/>\nb. I receive 57.16335 U.S dollars,<\/p>\n<p>Explanation:<br \/>\nGiven I am preparing for a trip to Canada. At the time of my trip,<br \/>\neach U.S dollar is worth 1.293 Canadian dollars and each<br \/>\nCanadian dollar is worth 0.773 U.S dollar.<br \/>\na. I exchange 150 U.S dollars for Canadian dollars ,<br \/>\nSo i receive Canadian dollars as 1.293 X 150 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a01,\u00a0 \u00a0 4,1<\/span><br \/>\n1.293&#8212;&#8211; 3 decimal places<br \/>\n<span style=\"text-decoration: underline;\">x150<br \/>\n<\/span>000000<br \/>\n064650<span style=\"text-decoration: underline;\"><br \/>\n129300<br \/>\n193.950&#8212;&#8211; 3 decimal places<br \/>\n<\/span>Therefore, I receive 193.95 Canadian dollars.<br \/>\nb. I spend 120 Canadian dollars on the trip. Then I exchange<br \/>\nthe remaining Canadian dollars for U.S dollars.<br \/>\nSo I have Canadian dollars left after my trip are<br \/>\n193.950 &#8211; 120 = 73.950, Now i will convert<br \/>\nCanadian dollars into U.S dollars as 73.950 X 0.773 =<br \/>\n<span style=\"text-decoration: underline;\">2,6,3\u00a0 \u00a0<\/span><br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 2,6,3\u00a0\u00a0<\/span><br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a02,1<\/span><br \/>\n73.950&#8212;- 3 decimal places<br \/>\n<span style=\"text-decoration: underline;\">X0.773&#8212;- 3 decimal places<\/span><br \/>\n00221850<br \/>\n05176500<br \/>\n51765000<br \/>\n<span style=\"text-decoration: underline;\">00000000<br \/>\n57.163350&#8212;-6 decimal places<br \/>\n<\/span>Therefore, I receive 57.16335 U.S dollars.<\/p>\n<p>Question 73.<br \/>\n<strong>OPEN-ENDED<\/strong><br \/>\nYou and four friends have dinner at a restaurant.<br \/>\na. Draw a restaurant menu that has main items, desserts, and beverages, with their prices.<br \/>\nb. Write a guest check that shows what each of you ate. Find the subtotal.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27342\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-273.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 273\" width=\"193\" height=\"250\" \/><br \/>\nc. Multiply by 0.07 to \ufb01nd the tax. Then \ufb01nd the total.<br \/>\nd. Round the total to the nearest whole number.<br \/>\nMultiply by 0.20 to estimate a tip. Including the tip,<br \/>\nhow much did the dinner cost?<br \/>\na.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-52172\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-73-1.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-73\" width=\"1331\" height=\"1191\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-73-1.bmp 1331w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-73-1-300x268.jpg 300w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-73-1-1024x916.jpg 1024w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-73-1-768x687.jpg 768w\" sizes=\"(max-width: 1331px) 100vw, 1331px\" \/><\/p>\n<p>b. Guest Check I ate Passion Mousse, Iced Coffee and<br \/>\nChicken Breasts Quarters only,<br \/>\nMy four friends ate Pecan Cheese Cake, Expresso and<br \/>\nMeatloaf with Gravy,<br \/>\nSubtotal is $75.95,<br \/>\nc. Including Tax amount the Total cost is $81.2665,<br \/>\nd. Including the tip, the dinner cost is $96,<\/p>\n<p>Explanation:<br \/>\na. Shown restaurant menu that has main items, desserts and<br \/>\nbeverages, with their prices.<br \/>\nb. I ate Passion Mousse, Iced Coffee and Chicken Breasts Quarters only,<br \/>\nmy friend ate Pecan Cheese Cake, Expresso and Meatloaf with Gravy,<br \/>\nNow Passion Mousse, Iced Coffee and Chicken Breasts Quarters only<br \/>\ncosts $5.90 + $5.90 + $3.75 =<br \/>\n5.90<br \/>\n5.90<span style=\"text-decoration: underline;\"><br \/>\n+3.75<br \/>\n15.55<br \/>\n<\/span>My cost is $15.55<br \/>\nand friend costs are Pecan Cheese Cake, Expresso and<br \/>\nMeatloaf with Gravy\u00a0 $4.95 + $5.90\u00a0 + $4.25 =<br \/>\n4.95<br \/>\n5.90<span style=\"text-decoration: underline;\"><br \/>\n+4.25<\/span><br \/>\n<span style=\"text-decoration: underline;\">15.10<br \/>\n<\/span>and friend costs are\u00a0 $15.10, and for 4 friends it is<br \/>\n4 X 15.10 =<br \/>\n<span style=\"text-decoration: underline;\">2<\/span><br \/>\n15.10&#8212;-2 decimal values<br \/>\n<span style=\"text-decoration: underline;\">X 4<br \/>\n60.40 &#8212;-2 decimal values<br \/>\n<\/span>For four friends it is $60.40,<span style=\"text-decoration: underline;\"><br \/>\n<\/span>Now Subtotal of mine and my four freind&#8217;s are<br \/>\n$15.55 + $60.40 =<br \/>\n15.55<br \/>\n<span style=\"text-decoration: underline;\">+60.40<\/span><br \/>\n<span style=\"text-decoration: underline;\">75.95<br \/>\n<\/span>Subtotal costs to $75.95<br \/>\nc. Given tax is 0.07, So tax on amount is<br \/>\n$75.95 X 0.07 =<br \/>\n<span style=\"text-decoration: underline;\">4,6,3<\/span><br \/>\n75.95&#8212;-2 decimal places<br \/>\n<span style=\"text-decoration: underline;\">X 0.07&#8212;2 decimal places<br \/>\n5.3165&#8211;4 decimal places<br \/>\n<\/span>So, The total amount after paying tax is $75.95 + $5.3165,<br \/>\n75.9500<br \/>\n<span style=\"text-decoration: underline;\">+5.3165<\/span><br \/>\n<span style=\"text-decoration: underline;\">81.2665<br \/>\n<\/span>Therefore, including tax amount the Total cost is $81.2665.<br \/>\nd. Rounding\u00a0 the total to the nearest whole number as<br \/>\n$81.2665 \u2248 $80, now multiplying\u00a0 by 0.20 we get<br \/>\n$80 X 0.20 = $16 is the tip.<br \/>\nIncluding the tip, the dinner cost is $80 + $16 = $96.<\/p>\n<p>Question 74.<br \/>\n<strong>GEOMETRY<\/strong><br \/>\nA rectangular painting has an area of 9.52 square feet.<br \/>\na. Draw three different ways in which this can happen.<br \/>\nb. The cost of a frame depends on the perimeter of the painting.<br \/>\nWhich of your drawings from part(a) is the least expensive to frame?<br \/>\nExplain your reasoning.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27343\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-274.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 274\" width=\"183\" height=\"245\" \/><br \/>\nc. The thin, black framing costs $1 per foot. The fancy framing costs $5 per foot. Will the fancy framing cost \ufb01ve times as much as the black framing? Explain why or why not.<br \/>\nd. Suppose the cost of a frame depends on the outside perimeter of the frame. Does this change your answer to part(c)? Explain why or why not.<br \/>\na.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-52211\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-74.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-74\" width=\"607\" height=\"208\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-74.bmp 607w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-74-300x103.jpg 300w\" sizes=\"(max-width: 607px) 100vw, 607px\" \/><br \/>\nb. Photoframe i (3.2, 2.975)\u00a0 is the least expensive to frame.<br \/>\nc. Yes, the fancy framing cost \ufb01ve times as much as the black framing,<br \/>\nd. Yes, It will change if it depends on the outside<br \/>\nperimeter of the frame, not on the material used.<\/p>\n<p>Explanation:<br \/>\na. Given a rectangular painting has an area of 9.52 square feet,<br \/>\nWe know area of rectangle is length X width and it is 9.52 square feet,<br \/>\nDrawn three different ways in which this can happen in the above picture,<br \/>\nas i. 3.2 X 2.975 = 9.52 square feet, ii. 3.4\u00a0 X 2.8 = 9.52 square feet and<br \/>\n3.8 X 2.505 = 9.52 square feet .<br \/>\nb. The perimeter of paintings are<br \/>\ni. 2(3.2 + 2.975) = 2 X 6.175 = 12.35 feet<br \/>\nii. 2(3.4 + 2.8) = 2 X 6.2 = 12.4 feet<br \/>\niii. 2( 3.8 + 2.505) = 2 X 6.305 = 12.61 feet<br \/>\namong the three the least perimeter is 12.35 feet,<br \/>\nSo, photoframe i(3.2, 2.975)\u00a0 is the least expensive to frame.<br \/>\nc. The thin, black framing costs $1 per foot.<br \/>\nThe fancy framing costs $5 per foot.<br \/>\nSo for black framing it is 9.52 X 1 =9.52 dollars,<br \/>\nand for fancy framing it costs 9.52 X 5 = 47.6 dollars,<br \/>\nwhich is 5 times more than black framing, therefore<br \/>\nfancy framing costs \ufb01ve times as much as the black framing.<br \/>\nd. If the cost of a frame depends on the outside perimeter of the frame<br \/>\nnot the material used then black framing and fancy frame will have<br \/>\nsame cost, which will differ from part c results.<\/p>\n<h3>Lesson 2.6 Dividing Whole Numbers<\/h3>\n<p><strong>EXPLORATION 1<\/strong><br \/>\n<strong>Using a Double Bar Graph<\/strong><br \/>\n<strong>Work with a partner. The double bar graph shows the history of a citywide cleanup day.<\/strong><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27344\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-275.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 275\" width=\"570\" height=\"347\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-275.png 570w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-275-300x183.png 300w\" sizes=\"(max-width: 570px) 100vw, 570px\" \/><br \/>\na. Make \ufb01ve conclusions from the graph.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27345\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-276.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 276\" width=\"321\" height=\"234\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-276.png 321w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-276-300x219.png 300w\" sizes=\"(max-width: 321px) 100vw, 321px\" \/><br \/>\nb. Compare the results of the city cleanup day in 2016 to the results in 2014.<br \/>\nc. What is the average combined amount of trash and recyclables collected each year over the four-year period?<br \/>\nd. Make a prediction about the amount of trash collected in a future year.<\/p>\n<p>a. Five conclusions from the graph:<br \/>\n1. Every year the amount of trash and recyclables<br \/>\nquantity is increasing.<br \/>\n2. Every year the trash quantity is more<br \/>\nthan the quantity of recyclables.<br \/>\n3. In the Year 2017 the amount of trash<br \/>\nand recyclables collected in pounds is more<br \/>\nthan 7000 pounds.<br \/>\n4. In the year 2014 he amount of trash<br \/>\nand recyclables collected in pounds is less<br \/>\nthan 3000 pounds.<br \/>\n5. We have collected information of data<br \/>\nfor 4 consecutive years.<\/p>\n<p>b.\u00a0 In\u00a02016 amount collected is 4970 + 732 = 5702 pounds and<br \/>\nin 2014 it is 2310 + 183 = 2493 pounds, Therefore in 2016 the<br \/>\namount collected\u00a0 is more compared to 2014.<\/p>\n<p>c. The average combined amount of trash and recyclables<br \/>\ncollected each year over the four-year period is 5052.5 pounds.<\/p>\n<p>d. We can predict about the amount of trash collected<br \/>\nin a future year 2018 will be approximately 7500 pounds.<\/p>\n<p>Explanation:<br \/>\na. Five conclusions from the graph are written as below<br \/>\n1. Every year the amount of trash and recyclables<br \/>\nquantity is increasing in 2014 it is 2310, 183,<br \/>\nin 2015 it is 3975,555, in 2016 it is 4970, 732 and<br \/>\nin year 2017 it is 6390, 1095 pounds.<br \/>\n2. Every year the trash quantity is more<br \/>\nthan the quantity of recyclables.<br \/>\nIn 2014 &#8211; 2310 &gt; 183,<br \/>\nIn 2015 &#8211; 3975 &gt; 555,<br \/>\nIn 2016 &#8211; 4970 &gt; 732,<br \/>\nIn 2017 &#8211; 6390 &gt; 1095.<br \/>\n3. In the Year 2017 the amount of trash<br \/>\nand recyclables collected in pounds is more<br \/>\nthan 7000 pounds because in 2017 it is 6390 + 1095 =<br \/>\n7485 pounds which is more than 7000 pounds.<br \/>\n4. In the year 2014 he amount of trash<br \/>\nand recyclables collected in pounds is less<br \/>\nthan 3000 pounds because in 2014 it is 2310 + 183<br \/>\n= 2493 pounds which is less than 3000 pounds.<br \/>\n5. We have collected information of data<br \/>\nfor 4 consecutive years as 2014 , 2015 , 2016 and 2017.<\/p>\n<p>b. In 2016 it is 4970 pounds of trash\u00a0 and 732 pounds of recyclables,<br \/>\nIn 2014 it is 2310 pounds of trash and 183 pounds of recyclables,<br \/>\nNow in n 2016 amount collected is 4970 + 732 = 5702 pounds and<br \/>\nin 2014 it is 2310 + 183 = 2493 pounds, Therefore in 2016 the<br \/>\namount collected\u00a0 is more compared to 2014.<\/p>\n<p>c. The average combined amount of trash and recyclables<br \/>\ncollected each year is<br \/>\nIn 2014 = 2310 + 183 = 2493 pounds<br \/>\nIn 2015 = 3975 + 555 = 4530 pounds<br \/>\nIn 2016 = 4970 + 732 = 5702 pounds<br \/>\nIn 2017 = 6390 + 1095 = 7485 pounds<br \/>\nTotal amount of collection in 4 years is<br \/>\n2493 + 4530 + 5702 + 7485 = 20210 pounds<br \/>\nand average for 4 years is 20210 \u00f7 4 = 5052.5 pounds,<br \/>\nTherefore the average combined amount of trash and recyclables<br \/>\ncollected each year over the four-year period is 5052.5 pounds.<\/p>\n<p>d. Every year we see how much it increased<br \/>\n2015 &amp; 2014- trash is 3975 &#8211; 2310 = 1665 pounds,<br \/>\nrecyclables is 555 &#8211; 183 = 372 pounds<br \/>\n2016 &amp; 2015 &#8211; trash 4970 &#8211; 3975 = 995 pounds<br \/>\nrecyclables is 732 &#8211; 555 = 177 pounds<br \/>\n2017 &amp; 2016 &#8211; trash 6390 &#8211; 4970 = 1420<br \/>\nrecyclables is 1095 &#8211; 732 = 363 pounds,<br \/>\nas we see every year trash has increased<br \/>\nSo we can predict about the amount of trash collected<br \/>\nin a future year 2018 will be approximately 7500 pounds.<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27346\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-277.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 277\" width=\"159\" height=\"209\" \/><br \/>\n<strong>2.6 Lesson<\/strong><\/p>\n<p>You have used long division to divide whole numbers. When the divisor divides evenly into the dividend, the quotient is a whole number.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27347\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-278.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 278\" width=\"248\" height=\"81\" \/><br \/>\nWhen the divisor does not divide evenly into the dividend, you obtain a remainder. When this occurs, you can write the quotient as a mixed number.<\/p>\n<p><strong>Try It<\/strong><br \/>\n<strong>Divide. Use estimation to check your answer.<\/strong><\/p>\n<p>Question 1.<br \/>\n234 \u00f7 9<br \/>\n234 \u00f7 9 = 26<br \/>\nEstimation is reasonable,<\/p>\n<p>Explanation:<br \/>\nGiven 234 \u00f7 9 =<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-52241\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-75.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-75\" width=\"286\" height=\"204\" \/><br \/>\n234 \u00f7 9 = 26,<br \/>\nEstimation is 230 \u00f7 9 = 25.555 \u2248 26,<br \/>\nSo estimation is reasonable.<\/p>\n<p>Question 2.<br \/>\n\\(\\frac{6096}{30}\\)<br \/>\n\\(\\frac{6096}{30}\\) = 203 and 6 remainder,<br \/>\nEstimation is reasonable,<\/p>\n<p>Explanation:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-52243\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-76.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-76\" width=\"286\" height=\"204\" \/><br \/>\n\\(\\frac{6096}{30}\\) = 203 and 6 remainder,<br \/>\nEstimation is \\(\\frac{6100}{30}\\) = 203.33 \u2248 203,<br \/>\nSo estimation is reasonable,<\/p>\n<p>Question 3.<br \/>\n45,691 \u00f7 28<br \/>\n45,691 \u00f7 28 = 1631 and remainder is 23,<br \/>\nEstimation is reasonable,<\/p>\n<p>Explanation:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-52248\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-77.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-77\" width=\"286\" height=\"312\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-77.bmp 286w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-77-275x300.jpg 275w\" sizes=\"(max-width: 286px) 100vw, 286px\" \/><br \/>\n45,691 \u00f7 28 = 1631 and remainder is 23,<br \/>\nEstimation is 45700 \u00f7 28 = 1632 \u2248 1631,<br \/>\nSo estimation is reasonable.<\/p>\n<p>Question 4.<br \/>\nFind the quotient of 9920 and 320.<br \/>\nThe quotient of 9920 and 320 is 31,<br \/>\nEstimation is reasonable,<\/p>\n<p>Explanation:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-52252\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-78.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-78\" width=\"286\" height=\"181\" \/><br \/>\nThe quotient of 9920 and 320 is 31,<br \/>\nEstimation is 9900 \u00f7 320 = 30.93 \u2248 31,<br \/>\nSo estimation is reasonable.<\/p>\n<p><strong>Try It<\/strong><\/p>\n<p>Question 5.<br \/>\n<strong>WHAT IF?<\/strong><br \/>\nYou make 30 equal payments for the go-kart.<br \/>\nTotal is $1380. How much is each payment?<br \/>\nEach payment is $46.<\/p>\n<p>Explanation:<br \/>\nGiven I make 30 equal payments for the go-kart.<br \/>\ntotal is $1380.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-52255\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-79-2.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-79\" width=\"286\" height=\"181\" \/><br \/>\nSo each payment is $46.<\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><\/p>\n<p>Solve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p><strong>DIVIDING WHOLE NUMBERS<\/strong><br \/>\n<strong>Divide. Use estimation to check your answer.<\/strong><\/p>\n<p>Question 6.<br \/>\n876 \u00f7 12<br \/>\n876 \u00f7 12 = 73,<br \/>\nEstimation is reasonable.<\/p>\n<p>Explanation:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-52256\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-80.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-80\" width=\"273\" height=\"181\" \/><br \/>\n876 \u00f7 12 = 73,<br \/>\nEstimation is 900 \u00f7 12 = 75 \u2248 73,<br \/>\nSo estimation is reasonable.<\/p>\n<p>Question 7.<br \/>\n3024 \u00f7 7<br \/>\n3024 \u00f7 7 = 432<br \/>\nEstimation is not reasonable,<\/p>\n<p>Explanation:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-52257\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-81.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-81\" width=\"286\" height=\"239\" \/><br \/>\n3024 \u00f7 7 = 432,<br \/>\nEstimation is 3000 \u00f7 7 = 428.5 \u2248 429 \u2260 432<br \/>\nSo, estimation is not reasonable.<\/p>\n<p>Question 8.<br \/>\n1043 \u00f7 22<br \/>\n1043 \u00f7 22 = 47 and remainder is 9,<br \/>\nEstimation is not reasonable.<\/p>\n<p>Explanation:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-52258\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-82.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-82\" width=\"286\" height=\"198\" \/><br \/>\n1043 \u00f7 22 = 47 and remainder is 9,<br \/>\nEstimation is 1000 \u00f7 22 = 45 and remainder is 10 \u2260<br \/>\n47 and remainder is 9, So, estimation is not reasonable.<\/p>\n<p>Question 9.<br \/>\n<strong>VOCABULARY<\/strong><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27348\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-279.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 279\" width=\"93\" height=\"84\" \/><br \/>\nUse the division problem shown to tell whether the number is the<br \/>\ndivisor, dividend, or quotient.<br \/>\na. 884 &#8212; dividend<br \/>\nb. 26 &#8212;quotient<br \/>\nc. 34 &#8212; divisor<\/p>\n<p>Explanation:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-52259\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-83.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-83\" width=\"286\" height=\"132\" \/><\/p>\n<p>In division, we divide a number by any other number to<br \/>\nget another number as a result. So, the number which is<br \/>\ngetting divided here is called the\u00a0dividend.<br \/>\nThe number which divides a given number is the\u00a0divisor.<br \/>\nAnd the number which we get as a result is known as the\u00a0quotient.<br \/>\nDivisor Formula: The operation of division in the form of:<br \/>\nDividend \u00f7 Divisor = Quotient,<br \/>\nThe above expression can also be written as:<br \/>\nDivisor = Dividend \u00f7 Quotient<br \/>\nHere, \u2018\u00f7\u2019 is the symbol of division. But sometimes,<br \/>\nit is also represented by the \u2018\/\u2019 symbol, such as<br \/>\nDividend \/ Divisor = Quotient.<\/p>\n<p>Question 10.<br \/>\n<strong>NUMBER SENSE<\/strong><br \/>\nWithout calculating, decide which is greater:<br \/>\n3999 \u00f7 129 or 3834 \u00f7 142. Explain.<br \/>\n3999 \u00f7 129 is greater,<\/p>\n<p>Explanation:<br \/>\nAs given to find\u00a0 which is greater among<br \/>\n3999 \u00f7 129 or 3834 \u00f7 142 if we compare<br \/>\nnumerators 3999 &gt; 3834 and denominators<br \/>\n129 &lt; 142 , So obviously 3999 \u00f7 129 is greater.<\/p>\n<p>Question 11.<br \/>\n<strong>REASONING<\/strong><br \/>\nIn a division problem, can the remainder be greater than the divisor? Explain.<\/p>\n<p>No, the remainder cannot be greater than the divisor,<\/p>\n<p>Explanation:<br \/>\n<span style=\"font-size: 16px;\">Remainder means something which is \u2018left over\u2019 or \u2018remaining\u2019.<br \/>\nWhen one number divides another number completely,<br \/>\nthe remainder is 0.<br \/>\n<\/span>The remainder is always less than the divisor.<br \/>\nIf the remainder is greater than the divisor,<br \/>\nit means that the division is incomplete,<br \/>\ntherefore the remainder cannot be greater than the divisor,<\/p>\n<p><strong>Self-Assessment for Problem Solving<\/strong><\/p>\n<p>Solve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 12.<br \/>\nIn a movie\u2019s opening weekend, 879,575 tickets are sold in 755 theaters.<br \/>\nThe average cost of a ticket is $9.50. What is the average amount of<br \/>\nmoney earned by each theater?<br \/>\nThe average amount of money earned by each theater is<br \/>\n$11067.5,<\/p>\n<p>Explanation:<br \/>\nGiven in a movie\u2019s opening weekend, 879,575 tickets are sold<br \/>\nin 755 theaters. So each theaters it is 879,575 \u00f7 755 = 1165<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-52274\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-85.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-85\" width=\"322\" height=\"306\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-85.bmp 322w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-85-300x285.jpg 300w\" sizes=\"(max-width: 322px) 100vw, 322px\" \/><br \/>\nNow the average cost of a ticket is $9.50 and we have<br \/>\neach theaters tickets sold are 1165, So average amount earned<br \/>\nis 1165 X $9.50 =<br \/>\n1165<br \/>\n<span style=\"text-decoration: underline;\">X9.50&#8212;- 2 decimal places<br \/>\n<\/span>0000000<br \/>\n0058250<br \/>\n<span style=\"text-decoration: underline;\">1048500<br \/>\n11067.50&#8212; 2 decimal places<br \/>\n<\/span>Therefore, the average amount of money earned by each theater is<br \/>\n$11067.5.<\/p>\n<p>Question 13.<br \/>\nA boat can carry 582 passengers to the base of a waterfall.<br \/>\nA total of 13,105 people ride the boat today.<br \/>\nAll the rides are full except for the \ufb01rst ride. How many rides are given?<br \/>\nHow many people are on the \ufb01rst ride?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27349\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-280.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 280\" width=\"189\" height=\"236\" \/><br \/>\nRides given are 22 and passengers on first ride are 301,<\/p>\n<p>Explanation:<br \/>\nGiven a\u00a0boat can carry 582 passengers to the base of a waterfall.<br \/>\nA total of 13,105 people ride the boat today.<br \/>\nSo rides given are 13,105 \u00f7 582 =<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-52276\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-86.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-86\" width=\"322\" height=\"193\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-86.bmp 322w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-86-300x180.jpg 300w\" sizes=\"(max-width: 322px) 100vw, 322px\" \/><br \/>\nGiven all the rides are full except for the \ufb01rst ride,<br \/>\nmeans total 22 rides and for first ride there are<br \/>\n301 passengers.<\/p>\n<p>Question 14.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nA new year begins at 12:00 A.M. on January 1.<br \/>\nWhat is the date and time 12,345 minutes after<br \/>\nthe start of a new year?<\/p>\n<p>The date is January 9<sup>th <\/sup>, time is 23:45 pm,<\/p>\n<p>Explanation:<br \/>\nGiven new year begins at 12:00 A.M. on January 1.<br \/>\nThe date and time 12,345 minutes after the start of a new year<br \/>\nwill be, first we convert into hours as 1 hour means<br \/>\n60 minutes, 12,345 \u00f7 60 =<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-52277\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-87.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-87\" width=\"322\" height=\"194\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-87.bmp 322w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-87-300x181.jpg 300w\" sizes=\"(max-width: 322px) 100vw, 322px\" \/><br \/>\n205 hours and 45 minutes, Now each day has 24 hours,<br \/>\nSo 205 \u00f7 24 =<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-52285\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-88-1.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-88\" width=\"317\" height=\"133\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-88-1.bmp 317w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-88-1-300x126.jpg 300w\" sizes=\"(max-width: 317px) 100vw, 317px\" \/><br \/>\nSo therefore it will be 8 complete days with<br \/>\n23 hours and 45 minutes,<br \/>\nthe date is January 9<sup>th <\/sup> , time is 23:45 pm.<\/p>\n<h3>Dividing Whole Numbers Homework &amp; Practice 2.6<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Multiply.<\/strong><\/p>\n<p>Question 1.<br \/>\n8 \u00d7 3.79<br \/>\n8 X 3.79 = 30.32<\/p>\n<p>Explanation:<br \/>\nGiven expression as 8 \u00d7 3.79 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a06,7<\/span><br \/>\n3.79&#8212;&#8212; 2 decimal places<br \/>\n<span style=\"text-decoration: underline;\">X\u00a0 8<br \/>\n30.32&#8212;&#8212; 2 decimal places<\/span><br \/>\nTherefore, 8 X 3.79 = 30.32.<\/p>\n<p>Question 2.<br \/>\n12.1 \u00d7 2.42<br \/>\n12.1 \u00d7 2.42 = 29.282<\/p>\n<p>Explanation:<br \/>\nGiven expression as 12.1 \u00d7 2.42 =<br \/>\n12.1&#8212;&#8212; 1 decimal place<br \/>\n<span style=\"text-decoration: underline;\">X 2.42&#8212;&#8211;2 decimal places<br \/>\n<\/span>00242<br \/>\n04840<br \/>\n<span style=\"text-decoration: underline;\">24200<br \/>\n29.282&#8212;&#8211;3 decimal places<\/span><br \/>\nTherefore, 12.1 \u00d7 2.42 = 29.282.<\/p>\n<p>Question 3.<br \/>\n6.43 \u00d7 0.28<br \/>\n6.43 \u00d7 0.28 = 1.8004<\/p>\n<p>Explanation:<br \/>\nGiven expression as 6.43 \u00d7 0.28 =<br \/>\n6.43&#8212;&#8212; 2 decimal places<br \/>\n<span style=\"text-decoration: underline;\">X 0.28&#8212;&#8211;2 decimal places<br \/>\n<\/span>005144<br \/>\n012860<br \/>\n<span style=\"text-decoration: underline;\">000000<br \/>\n1.8004&#8212;&#8211;4 decimal places<\/span><\/p>\n<p>Question 4.<br \/>\n9.526 . 6.61<br \/>\n9.526 X\u00a0 6.61 = 62.96686<\/p>\n<p>Explanation:<br \/>\nGiven expression as 9.526 \u00d7 6.61 =<br \/>\n9.526&#8212;&#8211; 3 decimal places<br \/>\n<span style=\"text-decoration: underline;\">X 6.61&#8212;&#8211;2 decimal places<br \/>\n<\/span>0009526<br \/>\n0571560<br \/>\n<span style=\"text-decoration: underline;\">5715600<br \/>\n62.96686&#8212;&#8211;5 decimal places<\/span><\/p>\n<p><strong>List the factor pairs of the number.<\/strong><\/p>\n<p>Question 5.<br \/>\n26.<br \/>\nFactors pairs of 26 = (1,26), (2, 13),<\/p>\n<p>Explanation:<br \/>\nFactors of 26 : 1, 2, 13, 26,<br \/>\nSo factor pairs of 26 are 1 x 26 or 2 x 13,<br \/>\n(1,26), (2, 13).<\/p>\n<p>Question 6.<br \/>\n72<br \/>\nFactors pairs of 72 are (1, 72) or (2, 36) or (3, 24) or<br \/>\n(4, 18) or (6, 12) or (8, 9).<\/p>\n<p>Explanation:<br \/>\nFactors of 72 : 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and 72,<br \/>\nSo factors pairs of 72 are (1, 72) or (2, 36) or (3, 24) or<br \/>\n(4, 18) or (6, 12) or (8, 9).<\/p>\n<p>Question 7.<br \/>\n50<br \/>\nFactors pairs of 50 are (1, 50), (2, 25) ,(5,10),<\/p>\n<p>Explanation:<br \/>\nFactors of 50 : 1, 2, 5,10, 25, and 50,<br \/>\nFactor pairs of 50 are (1, 50), (2, 25) ,(5,10).<\/p>\n<p>Question 8.<br \/>\n98<br \/>\nFactors pairs of 98 are (1, 98), (2, 49), (7, 14),<\/p>\n<p>Explanation:<br \/>\nFactors of 98 : 1, 2, 7, 14, 49, and 98,<br \/>\nFactors pairs of 98 are (1, 98), (2, 49), (7, 14).<\/p>\n<p><strong>Match the expression with its value.<\/strong><\/p>\n<p>Question 9.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27350\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-281.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 281\" width=\"73\" height=\"98\" \/><br \/>\n\\(\\frac{6}{7}\\) \u00a0\u00f7 \\(\\frac{3}{5}\\) = 1\\(\\frac{3}{7}\\),<br \/>\nmatches with B,<\/p>\n<p>Explanation:<br \/>\nGiven expressions as \\(\\frac{6}{7}\\) \u00a0\u00f7 \\(\\frac{3}{5}\\),<br \/>\nwe write reciprocal of the fraction \\(\\frac{3}{5}\\) as<br \/>\n\\(\\frac{5}{3}\\) and multiply as \\(\\frac{6}{7}\\) X \\(\\frac{4}{7}\\) =<br \/>\n\\(\\frac{6 X 5}{7 X 3}\\) = \\(\\frac{30}{21}\\),<br \/>\nas both goes in 3, 3 X 10 = 30, 3 X 7 = 21, \\(\\frac{30}{21}\\) =<br \/>\n\\(\\frac{10}{7}\\) as numerator is greater we write as<br \/>\n(1 X 7 + 3 by 7) = 1\\(\\frac{3}{7}\\) matches with B.<\/p>\n<p>Question 10.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27351\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-282.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 282\" width=\"67\" height=\"94\" \/><br \/>\n\\(\\frac{3}{7}\\) \u00a0\u00f7 \\(\\frac{6}{5}\\) = \\(\\frac{5}{14}\\),<br \/>\nmatches with C,<\/p>\n<p>Explanation:<br \/>\nGiven expressions as \\(\\frac{3}{7}\\) \u00a0\u00f7 \\(\\frac{6}{5}\\),<br \/>\nwe write reciprocal of the fraction \\(\\frac{6}{5}\\) as<br \/>\n\\(\\frac{5}{6}\\) and multiply as \\(\\frac{3}{7}\\) X \\(\\frac{5}{6}\\) =<br \/>\n\\(\\frac{3 X 5}{7 X 6}\\) = \\(\\frac{15}{42}\\),<br \/>\nas both goes in 3, 3 X 5 = 15, 3 X 14 = 42, \\(\\frac{15}{42}\\) =<br \/>\n\\(\\frac{5}{14}\\) matches with C.<\/p>\n<p>Question 11.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27352\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-283.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 283\" width=\"64\" height=\"89\" \/><br \/>\n\\(\\frac{6}{5}\\) \u00a0\u00f7 \\(\\frac{3}{7}\\) = 2\\(\\frac{4}{5}\\),<br \/>\nmatches with D,<\/p>\n<p>Explanation:<br \/>\nGiven expressions as \\(\\frac{6}{5}\\) \u00a0\u00f7 \\(\\frac{3}{7}\\),<br \/>\nwe write reciprocal of the fraction \\(\\frac{3}{7}\\) as<br \/>\n\\(\\frac{7}{3}\\) and multiply as \\(\\frac{6}{5}\\) X \\(\\frac{7}{3}\\) =<br \/>\n\\(\\frac{6 X 7}{5 X 3}\\) = \\(\\frac{42}{15}\\),<br \/>\nas both goes in 3, 3 X 14 = 72, 3 X 5 = 15, \\(\\frac{42}{15}\\) =<br \/>\n\\(\\frac{14}{5}\\) as numerator is greater we write as<br \/>\n(2 X 5 + 4 by 5) = 2\\(\\frac{4}{5}\\) matches with D.<\/p>\n<p>Question 12.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27353\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-284.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 284\" width=\"74\" height=\"92\" \/><br \/>\n\\(\\frac{3}{5}\\) \u00a0\u00f7 \\(\\frac{6}{7}\\) = \\(\\frac{7}{10}\\),,<br \/>\nmatches with A,<\/p>\n<p>Explanation:<br \/>\nGiven expressions as \\(\\frac{3}{5}\\) \u00a0\u00f7 \\(\\frac{6}{7}\\),<br \/>\nwe write reciprocal of the fraction \\(\\frac{6}{7}\\) as<br \/>\n\\(\\frac{7}{6}\\) and multiply as \\(\\frac{3}{5}\\) X \\(\\frac{7}{6}\\) =<br \/>\n\\(\\frac{3 X 7}{5 X 6}\\) = \\(\\frac{21}{30}\\),<br \/>\nas both goes in 3, 3 X 7 = 21, 3 X 10 = 30, \\(\\frac{21}{30}\\) =<br \/>\n\\(\\frac{7}{10}\\) matches with A.<\/p>\n<p><strong>Concepts, Skills, &amp; Problem Solving<\/strong><br \/>\n<strong>OPERATIONS WITH WHOLE NUMBERS<\/strong><br \/>\n<strong>The bar graph shows the attendance at a food festival. Use the graph to answer the question.<\/strong> (See Exploration 1, p. 81.)<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27354\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-285.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 285\" width=\"342\" height=\"338\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-285.png 342w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-285-300x296.png 300w\" sizes=\"(max-width: 342px) 100vw, 342px\" \/><\/p>\n<p>Question 13.<br \/>\nWhat is the total attendance at the food festival from 2014 to 2017?<\/p>\n<p>The total attendance at the food festival from<br \/>\n2014 to 2017 is 16,648,<\/p>\n<p>Explanation:<br \/>\nAs shown in bar graph we add attendance from<br \/>\nyear 2014 to 2017 as 2118 + 3391 + 4785 + 6354 =<br \/>\n2118<br \/>\n3391<br \/>\n4785<br \/>\n<span style=\"text-decoration: underline;\">+6354<\/span><br \/>\n<span style=\"text-decoration: underline;\">16,648<br \/>\n<\/span>Therefore ,the total attendance at the food festival from<br \/>\n2014 to 2017 is 16,648.<\/p>\n<p>Question 14.<br \/>\nHow many times more people attended the food festival in 2017 than in 2014?<\/p>\n<p>4,236 more people attended the food festival in 2017,<\/p>\n<p>Explanation:<br \/>\nIn Year 2017 people attended the food festival are 6354 and<br \/>\nin year 2014 it is 2118, So more people attended the food festival<br \/>\nin 2017 are 6354 &#8211; 2118 =<br \/>\n6354<br \/>\n<span style=\"text-decoration: underline;\">-2118<br \/>\n4236<br \/>\n<\/span>So, 4,236 more people attended the food festival in 2017.<\/p>\n<p>Question 15.<br \/>\nWhat is the average attendance at the festival each year over the four-year period?<\/p>\n<p>The average attendance at the festival each year<br \/>\nover the four-year period is 4162,<\/p>\n<p>Explanation:<br \/>\nWe have total attendance at the food festival from<br \/>\n2014 to 2017 is 16,648, Now the average attendance is<br \/>\n16648 \u00f7 4 = 4162<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-52303\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-89.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-89\" width=\"288\" height=\"310\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-89.bmp 288w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-89-279x300.jpg 279w\" sizes=\"(max-width: 288px) 100vw, 288px\" \/><br \/>\nTherefore, The average attendance at the festival each year<br \/>\nover the four-year period is 4162.<\/p>\n<p>Question 16.<br \/>\nThe festival projects that the attendance for 2018 will be<br \/>\ntwice the attendance in 2016. What is the<br \/>\nprojected attendance for 2018?<\/p>\n<p>The projected attendance for 2018 is 9570,<\/p>\n<p>Explanation:<br \/>\nGiven the attendance in 2016 is 4785,<br \/>\nthe projected attendance for 2018 is<br \/>\ntwice the attendance in 2016 is 2 X 4785 = 9570.<br \/>\nTherefore, the projected attendance for 2018 is 9570.<\/p>\n<p><strong>DIVIDING WHOLE NUMBERS<\/strong><br \/>\n<strong>Divide. Use estimation to check your answer.<\/strong><\/p>\n<p>Question 17.<br \/>\n837 \u00f7 27<br \/>\n837 \u00f7 27 = 31,<\/p>\n<p>Explanation:<br \/>\nGiven expression as 837 \u00f7 27 =<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-52304\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-90.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-90\" width=\"288\" height=\"190\" \/><br \/>\nSo, 837 \u00f7 27 = 31.<\/p>\n<p>Question 18.<br \/>\n1088 \u00f7 34<br \/>\n1088 \u00f7 34 = 32,<\/p>\n<p>Explanation:<br \/>\nGiven expression as 1088 \u00f7 34 =<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-52305\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-91.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-91\" width=\"288\" height=\"190\" \/><br \/>\nTherefore, 1088 \u00f7 34 = 32.<\/p>\n<p>Question 19.<br \/>\n903 \u00f7 72<br \/>\n903 \u00f7 72 = 12\\(\\frac{13}{24}\\),<\/p>\n<p>Explanation:<br \/>\nGiven \\(\\frac{903}{72}\\) as both goes in 3,<br \/>\n3 X 301, 3 X 24 = 72, (301, 24) = \\(\\frac{301}{24}\\) as<br \/>\nnumerator is greater we write as (12 X 24 + 13 by 24) =<br \/>\n12\\(\\frac{13}{24}\\).<\/p>\n<p>Question 20.<br \/>\n6409 \u00f7 61<br \/>\n6409 \u00f7 61 = 105\\(\\frac{4}{61}\\),<\/p>\n<p>Explanation:<br \/>\nGiven \\(\\frac{6409}{61}\\)\u00a0as<br \/>\nnumerator is greater we write as (105 X 61 + 4 by 61) =<br \/>\n105\\(\\frac{4}{61}\\).<\/p>\n<p>Question 21.<br \/>\n\\(\\frac{5986}{82}\\)<br \/>\n\\(\\frac{5986}{82}\\) = 73,<\/p>\n<p>Explanation:<br \/>\nGiven \\(\\frac{5986}{82}\\) as both goes in 82,<br \/>\n82 X 73 = 5986 we get \\(\\frac{5986}{82}\\) = 73.<\/p>\n<p>Question 22.<br \/>\n6200 \u00f7 163<br \/>\n6200 \u00f7 163 = 38\\(\\frac{6}{163}\\)<\/p>\n<p>Explanation:<br \/>\nGiven expression as \\(\\frac{6200}{163}\\) here<br \/>\nnumerator is greater we write as ( 38 X 163\u00a0 + 6 by 163) =<br \/>\n38\\(\\frac{6}{163}\\).<\/p>\n<p>Question 23.<br \/>\n6255 \u00f7 118<br \/>\n6255 \u00f7 118 = 53\\(\\frac{1}{118}\\)<\/p>\n<p>Explanation:<br \/>\nGiven expression as \\(\\frac{6255}{118}\\), here<br \/>\nnumerator is greater we write as (53 X 118 + 1 by 118) =<br \/>\n53\\(\\frac{1}{118}\\).<\/p>\n<p>Question 24.<br \/>\n\\(\\frac{588}{84}\\)<br \/>\n\\(\\frac{588}{84}\\) = 7<\/p>\n<p>Explanation:<br \/>\nGiven expression as \\(\\frac{588}{84}\\) as<br \/>\nboth goes in 84, 84 X 7 = 588, 84 X 1 = 84,<br \/>\nSo \\(\\frac{588}{84}\\) = 7.<\/p>\n<p>Question 25.<br \/>\n7440 \u00f7 124<br \/>\n7440 \u00f7 124 = 60<\/p>\n<p>Explanation:<br \/>\nGiven expression as \\(\\frac{7440{124}\\), here<br \/>\nboth goes in 124 as 124 X 60 = 7440, 124 X 1 = 124, (60, 1),<br \/>\ntherefore \\(\\frac{7440{124}\\) = 60.<\/p>\n<p>Question 26.<br \/>\n26,862 \u00f7 407<br \/>\n26,862 \u00f7 407 = 66<\/p>\n<p>Explanation:<br \/>\nGiven expression as \\(\\frac{26862}{407}\\), here<br \/>\nboth goes in 407 as 407 X 66 = 26862, 407 X 1 = 407, (66, 1),<br \/>\ntherefore \\(\\frac{26862}{407}\\) = 66.<\/p>\n<p>Question 27.<br \/>\n8241 \u00f7 173<br \/>\n8241 \u00f7 173 = 47\\(\\frac{110}{173}\\),<\/p>\n<p>Explanation:<br \/>\nGiven expression as \\(\\frac{8241}{173}\\),<br \/>\nnumerator is greater so we write as (47 X 173 + 110 by 173),<br \/>\n\\(\\frac{8241}{173}\\) = 47\\(\\frac{110}{173}\\).<\/p>\n<p>Question 28.<br \/>\n\\(\\frac{33,505}{16}\\)<br \/>\n\\(\\frac{33,505}{16}\\) = 2094\\(\\frac{1}{16}\\),<\/p>\n<p>Explanation:<br \/>\nGiven expression as \\(\\frac{33505}{16}\\),<br \/>\nnumerator is greater so we write as (2094 X 16 + 1 by 16),<br \/>\ntherefore \\(\\frac{33505}{16}\\) = 2094\\(\\frac{1}{16}\\).<\/p>\n<p>Question 29.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nA pharmacist divides 364 pills into prescription bottles.<br \/>\nEach bottle contains 28 pills. How many bottles does<br \/>\nthe pharmacist \ufb01ll?<\/p>\n<p>The pharmacist fills 13 bottles,<\/p>\n<p>Explanation:<br \/>\nGiven a\u00a0pharmacist divides 364 pills into prescription bottles.<br \/>\nEach bottle contains 28 pills, number of bottles the pharmacist fill<br \/>\nare 364 \u00f7 28 = 13,<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-52320\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-92.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-92\" width=\"288\" height=\"201\" \/><br \/>\ntherefore, the pharmacist fills 13 bottles.<\/p>\n<p><strong>YOU BE THE TEACHER<\/strong><br \/>\n<strong>Your friend \ufb01nds the quotient. Is your friend correct? Explain your reasoning.<\/strong><\/p>\n<p>Question 30.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27355\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-286.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 286\" width=\"133\" height=\"154\" \/><br \/>\nNo, friend is incorrect as 963 \u00f7 8 = 120 and remainder is 3<br \/>\n\u2260 12 remainder 3,<\/p>\n<p>Explanation:<br \/>\nGiven expression as \\(\\frac{963}{8}\\),<br \/>\nnumerator is greater so we write as ( 120 X 8 + 3 by 8),<br \/>\ntherefore \\(\\frac{963}{16}\\) = 120\\(\\frac{3}{8}\\) \u2260<br \/>\n12 remainder 3, So friend is incorrect.<\/p>\n<p>Question 31.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27356\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-287.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 287\" width=\"140\" height=\"161\" \/><br \/>\nNo, friend is incorrect as 1308 \u00f7 12 = 109 \u2260 19,<\/p>\n<p>Explanation:<br \/>\nGiven expression as \\(\\frac{1308}{12}\\),<br \/>\nnumerator is greater and 12 X 109 = 1308<br \/>\ntherefore \\(\\frac{1308}{12}\\) = 109 \u2260 19,<br \/>\nSo friend is incorrect.<\/p>\n<p><strong>GEOMETRY<\/strong><br \/>\n<strong>Find the perimeter of the rectangle.<\/strong><\/p>\n<p>Question 32.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27357\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-288.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 288\" width=\"127\" height=\"106\" \/><br \/>\nThe perimeter of the rectangle is 24 inches,<\/p>\n<p>Explanation:<br \/>\nGiven area of rectangle as 35 in<sup>2 <\/sup>and width as 7 in,<br \/>\nwe know area of rectangle is width X length,<br \/>\n35 = 7 X length, So length = 35 \u00f7 7 = 5 ( 7 X 5 = 35),<br \/>\nSo length of rectangle is 5 in, Now perimeter of<br \/>\nthe rectangle is 2( length + width) = 2, (5 + 7) =<br \/>\n2 X 12 = 24 inches, therefore the perimeter of the<br \/>\nrectangle is 24 inches.<\/p>\n<p>Question 33.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27358\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-289.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 289\" width=\"156\" height=\"150\" \/><br \/>\nThe perimeter of the rectangle is 42 ft,<\/p>\n<p>Explanation:<br \/>\nGiven area of rectangle as 108 ft<sup>2 <\/sup>and width as 12 ft,<br \/>\nwe know area of rectangle is width X length,<br \/>\n108 = 12 X length, So length = 108 \u00f7 12 = 9, ( 9 X 12 = 108),<br \/>\nSo length of rectangle is 9 ft, Now perimeter of<br \/>\nthe rectangle is 2( length + width) = 2 (9 + 12) = 2 X 21 = 42 ft,<br \/>\ntherefore the perimeter of the rectangle is 42 ft.<\/p>\n<p>Question 34.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27359\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-290.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 290\" width=\"148\" height=\"143\" \/><\/p>\n<p>The perimeter of the rectangle is 36 m,<\/p>\n<p>Explanation:<br \/>\nGiven area of rectangle as 80 m<sup>2 <\/sup>and width as 10 m,<br \/>\nwe know area of rectangle is width X length,<br \/>\n80 = 10 X length, So length = 80 \u00f7 10 = 8, (8 X 10 = 80),<br \/>\nSo length of rectangle is 8 m, Now perimeter of<br \/>\nthe rectangle is 2( length + width) = 2 (8 + 10) = 2 X 18 = 36 m,<br \/>\ntherefore the perimeter of the rectangle is 36 m.<\/p>\n<p>Question 35.<br \/>\n<strong>REASONING<\/strong><br \/>\nYou borrow bookcases like the one shown to display 943 books<br \/>\nat a book sale. You plan to put 22 books on each shelf.<br \/>\nNo books will be on top of the bookcases.<br \/>\na. How many bookcases must you borrow to display all the books?<br \/>\nb. You \ufb01ll the shelves of each bookcase in order, starting<br \/>\nwith the top shelf. How many books are on each shelf of the<br \/>\nlast bookcase?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27360\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-291.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 291\" width=\"166\" height=\"249\" \/><br \/>\na. 9 bookcases I must borrow to display all the books,<br \/>\nb. Books in\u00a0 each shelf of the last bookcase are<br \/>\nshelf 1-22, shelf\u00a0 2- 22, shelf 3-19, shelf 4-0, shelf 5 -0 books,<\/p>\n<p>Explanation:<br \/>\nGiven I borrow bookcases like the one shown to display<br \/>\n943 books at a book sale.I plan to put 22 books on each<br \/>\nshelf and no books will be on top of the bookcases.<br \/>\na. Number of \u00a0bookcases I must borrow to display<br \/>\nall the books are each bookcases have 5 shelves and in each<br \/>\nshelf I can put 22 books so in each bookcase I can put<br \/>\n5 X 22 = 110 books, Now 943 \u00f7 110 =<br \/>\n\\(\\frac{943}{110}\\) as numerator is greater we<br \/>\nwrite as ( 8 X 110 + 63 by 110) = 8\\(\\frac{63}{110}\\) ,<br \/>\nmeans 8 bookcases and 63 books are still there,<br \/>\nso I require 9 bookcases to completely keep the books<br \/>\nin the shelves.<br \/>\nb. Now I \ufb01ll the shelves of each bookcase in order, starting<br \/>\nwith the top shelf. I have 63 books to arrange in 9 bookcase,<br \/>\nSo books are on each shelf of the last bookcase are<br \/>\nshelf 1 &#8211; 22 books, now we are left with \u00a063 &#8211; 22 = 41 books<br \/>\nshelf 2 = 22 books, now we are left with 41 &#8211; 22 = 19 books<br \/>\nshelf 3 = 19 books,<br \/>\nshelf 4 = 0 books,<br \/>\nshelf 5 = 0 books respectively.<\/p>\n<p>Question 36.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nThe siding of a house is 2250 square feet. The siding needs two coats of paint.<br \/>\na. What is the minimum cost of the paint needed to complete the job?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27361\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-292.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 292\" width=\"313\" height=\"115\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-292.png 313w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-292-300x110.png 300w\" sizes=\"(max-width: 313px) 100vw, 313px\" \/><br \/>\nb. How much paint is left over when you spend the minimum amount?<\/p>\n<p>a. The minimum cost of the paint needed to complete the job is $435,<br \/>\nb. \\(\\frac{30}{32}\\) gallon paint is left over<br \/>\nwhen I spend the minimum amount,<\/p>\n<p>Explanation:<br \/>\nGiven the siding of a house is 2250 square feet.<br \/>\nThe siding needs two coats of paint. So the siding<br \/>\nbecomes 2 X 2250 = 4500 square feet,<br \/>\nNow we check with the paints needed If we take<br \/>\n1 quart it will cover 80 square feet and 1 quart cost is $ 18 means<br \/>\nwe require 4500 \u00f7 80 = \\(\\frac{4500}{80}\\) as both goes<br \/>\nin 10, 10 X 450 = 4500, 10 X 8 = 80, (450 , 8) = \\(\\frac{450}{8}\\)<br \/>\nas numerator is greater we write as ( 56 X 8 + 2 by 8) = 56\\(\\frac{2}{8}\\) ,<br \/>\nwe need approximately 57 quart, the cost will be<br \/>\n57 X $18 = $1026 to complete the job,<br \/>\nIf we take 1 gallon it will cover 320 square feet and<br \/>\n1 gallon costs is $29 means we require 4500 \u00f7 320 =<br \/>\n\\(\\frac{4500}{320}\\) as both goes in 10, 10 X 450 = 4500,<br \/>\n10 X 32 = 320, (450 , 32) = \\(\\frac{450}{32}\\)<br \/>\nas numerator is greater we write as ( 14 X 32 + 2 by 32) = 14\\(\\frac{2}{32}\\) ,<br \/>\nwe need approximately 15 gallons, the cost will be<br \/>\n15 X $29 = $435 to complete the job,<br \/>\nSo the minimum cost of the paint needed to complete the job is $435.<br \/>\nb. The paint left over when I spend the minimum amount is<br \/>\n15 &#8211;\u00a0 \\(\\frac{450}{32}\\) = (15 X 32 &#8211; 450 by 32) =<br \/>\n(480-450 by 32) = \\(\\frac{30}{32}\\) gallon paint is left.<\/p>\n<p>Question 37.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nUse the digits 3, 4, 6, and 9 to complete the division problem. Use each digit once.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27362\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-293.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 293\" width=\"240\" height=\"55\" \/><br \/>\n36,000 \u00f7 900 = 40 or 36,000 \u00f7 400 = 90,<\/p>\n<p>Explanation:<br \/>\nTo complete the division problem we use digits<br \/>\n3, 4, 6, 9 each digit once as if we take first 3,4,<br \/>\nwe are left with digits 6, 9,<br \/>\n34,000 \u00f7 900 \u2248 38 not matches to complete the division problem,<br \/>\n34,000 \u00f7 600 \u2248 57 not matches to complete the division problem,<br \/>\nnext 36,000 \u00f7 900 = 40 matches to complete the division problem,<br \/>\n36,000 \u00f7 400 = 90 matches to complete the division problem,<br \/>\nnext we take 4, 3 we are left with digits 6 ,9,<br \/>\n43,000 \u00f7 900 \u2248 47 not matches to complete the division problem,<br \/>\n43,000 \u00f7 600 \u2248 71 not matches to complete the division problem,<br \/>\nnext we take 6, 4\u00a0 we are left with digits 3 ,9,<br \/>\n64,000 \u00f7 300 \u2248 213 not matches to complete the division problem,<br \/>\n64,000 \u00f7 900 \u2248 71 not matches to complete the division problem,<br \/>\nnext we take 9, 6 we are left with digits 3,4,<br \/>\n96,000 \u00f7 300 \u2248 320 not matches to complete the division problem,<br \/>\n96,000 \u00f7 400 \u2248 240 not matches to complete the division problem,<br \/>\nSo to complete the division problem we write as<br \/>\n36,000 \u00f7 900 = 40 or 36,000 \u00f7 400 = 90.<\/p>\n<h3>Lesson 2.7 Dividing Decimals<\/h3>\n<p><strong>EXPLORATION 1<\/strong><br \/>\n<strong>Dividing Decimals<\/strong><br \/>\n<strong>Work with a partner.<\/strong><br \/>\na. Write two division expressions represented by each area model. Then \ufb01nd the quotients. Explain how you found your answer.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27363\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-294.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 294\" width=\"416\" height=\"381\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-294.png 416w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-294-300x275.png 300w\" sizes=\"(max-width: 416px) 100vw, 416px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27364\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-295.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 295\" width=\"624\" height=\"273\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-295.png 624w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-295-300x131.png 300w\" sizes=\"(max-width: 624px) 100vw, 624px\" \/><br \/>\nb. Use a calculator to \ufb01nd 119 \u00f7 17, 11.9 \u00f7 1.7, 1.19 \u00f7 0.17<br \/>\nand 0.119 \u00f7 0.017. What do you notice? Explain how you can<br \/>\nuse long division to divide any pair of multi-digit decimals.<\/p>\n<p>a. i. Two division expressions are \\(\\frac{40}{10}\\) \u00f7 \\(\\frac{8}{10}\\) =<br \/>\n\\(\\frac{5}{10}\\) or \\(\\frac{40}{100}\\)\u00a0 \u00f7 \\(\\frac{5}{10}\\) =<br \/>\n\\(\\frac{8}{10}\\),<\/p>\n<p>ii. The division expression of whole part is<br \/>\n\\(\\frac{50}{100}\\) \u00f7 \\(\\frac{5}{10}\\) =\u00a0 \\(\\frac{10}{10}\\) or<br \/>\nand \\(\\frac{50}{100}\\) \u00f7 \\(\\frac{10}{10}\\) = \\(\\frac{5}{10}\\)<br \/>\ndecimal part is \\(\\frac{25}{10}\\) \u00f7 \\(\\frac{5}{10}\\) = \\(\\frac{5}{10}\\)<br \/>\nor \\(\\frac{25}{10}\\) \u00f7 \\(\\frac{5}{10}\\) = \\(\\frac{5}{10}\\),<\/p>\n<p>iii. The division expression of whole part is<br \/>\n\\(\\frac{70}{100}\\) \u00f7 \u00a0\\(\\frac{7}{10}\\) = \\(\\frac{10}{10}\\) or<br \/>\n\\(\\frac{70}{100}\\) \u00f7 \u00a0\\(\\frac{10}{10}\\) = \\(\\frac{7}{10}\\) and<br \/>\ndecimal part is \\(\\frac{49}{10}\\) \u00f7 \\(\\frac{7}{10}\\) = \\(\\frac{7}{10}\\),<\/p>\n<p>b. 19 \u00f7 17 = 7, 11.9 \u00f7 1.7 = 7, 1.19 \u00f7 0.17 = 7<br \/>\nand 0.119 \u00f7 0.017 = 7,<br \/>\nTo multiply\u00a0decimals, first multiply as<br \/>\nif there is no\u00a0decimal. Next, count the number of\u00a0digits\u00a0after<br \/>\nthe\u00a0decimal\u00a0in each factor. Finally, put the same number of\u00a0digits<br \/>\nbehind the\u00a0decimal\u00a0in the product.<\/p>\n<p>Explanation:<br \/>\na. Two division expressions are \\(\\frac{40}{10}\\) \u00f7 \\(\\frac{8}{10}\\) =<br \/>\n\\(\\frac{5}{10}\\) or \\(\\frac{40}{100}\\)\u00a0 \u00f7 \\(\\frac{5}{10}\\) =<br \/>\n\\(\\frac{8}{10}\\), or<br \/>\nBy counting the blocks in the area model found<br \/>\nthe two division expressions are \\(\\frac{5}{10}\\) \u00f7 \\(\\frac{10}{8}\\)<br \/>\nfirst we write the reciprocal \\(\\frac{10}{8}\\) and multiply as<br \/>\n\\(\\frac{5}{10}\\) X \\(\\frac{8}{10}\\)<br \/>\nand Step I: We multiply the numerators as 5 X 8 = 40<br \/>\nStep II: We multiply the denominators as 10 X 10 =100<br \/>\nStep III: We write the fraction in the simplest form as<br \/>\n\\(\\frac{40}{100}\\), So \\(\\frac{5 X 8}{10 X 10}\\) = \\(\\frac{40}{100}\\).<br \/>\nIf we see the area model the purple color blocks show<br \/>\n40 out of 100 blocks.<br \/>\nii. The division expression of whole part is<br \/>\n\\(\\frac{50}{100}\\) \u00f7 \\(\\frac{5}{10}\\) =\u00a0 \\(\\frac{10}{10}\\) or<br \/>\nand \\(\\frac{50}{100}\\) \u00f7 \\(\\frac{10}{10}\\) = \\(\\frac{5}{10}\\)<br \/>\ndecimal part is \\(\\frac{25}{10}\\) \u00f7 \\(\\frac{5}{10}\\) = \\(\\frac{5}{10}\\)<br \/>\nor \\(\\frac{25}{10}\\) \u00f7 \\(\\frac{5}{10}\\) = \\(\\frac{5}{10}\\), or<br \/>\nBy counting the blocks in the area model found<br \/>\nthe multiplication expression as \\(\\frac{10}{10}\\) \u00f7 \\(\\frac{5}{10}\\)<br \/>\nfirst we write the reciprocal \\(\\frac{10}{5}\\) and multiply as<br \/>\n\\(\\frac{10}{10}\\) X \\(\\frac{5}{10}\\)<br \/>\nand Step I: We multiply the numerators as 10 X 5 = 50<br \/>\nStep II: We multiply the denominators as 10 X 10 =100<br \/>\nStep III: We write the fraction in the simplest form as<br \/>\n\\(\\frac{50}{100}\\), So \\(\\frac{10 X 5}{10 X 10}\\) = \\(\\frac{50}{100}\\).<br \/>\nNow in decimal part we have \\(\\frac{5}{10}\\) \u00f7 \\(\\frac{10}{5}\\),<br \/>\nfirst we write the reciprocal \\(\\frac{10}{5}\\) and multiply as<br \/>\n\\(\\frac{5}{10}\\) X \\(\\frac{5}{10}\\)<br \/>\nsimilar to whole part we do multiplication<br \/>\nStep I: We multiply the numerators as 5 X 5 = 25<br \/>\nStep II: We multiply the denominators as 10 X 10 =100<br \/>\nStep III: We write the fraction in the simplest form as<br \/>\n\\(\\frac{25}{100}\\), therefore then the product results is<br \/>\n\\(\\frac{50}{100}\\) + \\(\\frac{25}{100}\\),<\/p>\n<p>iii. The division expression of whole part is<br \/>\n\\(\\frac{70}{100}\\) \u00f7 \u00a0\\(\\frac{7}{10}\\) = \\(\\frac{10}{10}\\) or<br \/>\n\\(\\frac{70}{100}\\) \u00f7 \u00a0\\(\\frac{10}{10}\\) = \\(\\frac{7}{10}\\) and<br \/>\ndecimal part is \\(\\frac{49}{10}\\) \u00f7 \\(\\frac{7}{10}\\) = \\(\\frac{7}{10}\\), or By counting the blocks in the area model found<br \/>\nthe division expression as \\(\\frac{10}{10}\\) \u00f7 \\(\\frac{10}{7}\\)<br \/>\nfirst we write the reciprocal \\(\\frac{10}{7}\\) and multiply as<br \/>\n\\(\\frac{10}{10}\\) X \\(\\frac{7}{10}\\)<br \/>\nand Step I: We multiply the numerators as 10 X 7 = 70<br \/>\nStep II: We multiply the denominators as 10 X 10 =100<br \/>\nStep III: We write the fraction in the simplest form as<br \/>\n\\(\\frac{70}{100}\\), So \\(\\frac{10 X 7}{10 X 10}\\) = \\(\\frac{70}{100}\\).<br \/>\nNow in decimal part we have \\(\\frac{7}{10}\\) \u00f7 \\(\\frac{10}{7}\\),<br \/>\nfirst we write the reciprocal \\(\\frac{10}{7}\\) and multiply as<br \/>\n\\(\\frac{7}{10}\\) X \\(\\frac{7}{10}\\),<br \/>\nsimilar to whole part we do multiplication<br \/>\nStep I: We multiply the numerators as 7 X 7 = 49<br \/>\nStep II: We multiply the denominators as 10 X 10 =100<br \/>\nStep III: We write the fraction in the simplest form as<br \/>\n\\(\\frac{49}{100}\\), therefore then the product results is<br \/>\n\\(\\frac{70}{100}\\) + \\(\\frac{49}{100}\\).<\/p>\n<p>b. 19 \u00f7 17 = 7, 11.9 \u00f7 1.7 = 7, 1.19 \u00f7 0.17 = 7<br \/>\nand 0.119 \u00f7 0.017 = 7,<br \/>\nTo multiply\u00a0decimals, first multiply as<br \/>\nif there is no\u00a0decimal. Next, count the number of\u00a0digits\u00a0after<br \/>\nthe\u00a0decimal\u00a0in each factor. Finally, put the same number of\u00a0digits<br \/>\nbehind the decimal in the product.<br \/>\nExample: 7.6)19.76(<br \/>\nThe first thing that we want to do when dividing decimals is to turn<br \/>\nthe divisor into a whole number. We do this by moving the decimal<br \/>\nplace to the right:<span class=\"Apple-converted-space\"><br \/>\n7.6 &#8212;&#8211;&gt; 76<\/span><\/p>\n<p class=\"p1\">If we move the decimal over\u00a0one\u00a0place in the divisor,<br \/>\nwe must also move the decimal over\u00a0one\u00a0place in the dividend:<br \/>\n19.76 &#8212;&#8211;&gt;197.6<\/p>\n<p class=\"p1\">The new division problem should look as follows:\u00a0<span class=\"Apple-converted-space\"><br \/>\n76 )197.6(<br \/>\n<\/span>We&#8217;ve already placed the decimal in our answer.<br \/>\nWhen we divide decimals, we place the decimal directly above<br \/>\nthe decimal in the dividend, but only after we&#8217;ve completed the<br \/>\nfirst two steps of moving the decimal point in the divisor and dividend.<\/p>\n<p class=\"p1\">Now we can divide like normal: 76)197.6(<br \/>\nThink: how many times can 76 go into 197<br \/>\n76 can go into 197\u00a0two times so we write a 2 over the\u00a07<br \/>\nin the dividend:<br \/>\n76) 197.6(2.<br \/>\nNext, we multiply 2 and 76 and write that product underneath<br \/>\nthe 197 and subtract:<br \/>\n76)197.6(2.<br \/>\n<span style=\"text-decoration: underline;\"> \u00a0 -152\u00a0 \u00a0<\/span><br \/>\n45<\/p>\n<p class=\"p2\">Now we bring down the 6 from the dividend to make the 45 into a 456.<\/p>\n<p class=\"p1\">Think: how many times can 76 go into 456?<\/p>\n<p class=\"p1\">76 can go into 465 six times so we write a 6 above the 6 in the dividend:<br \/>\n76)197.6(2.6<br \/>\n<span style=\"text-decoration: underline;\"> \u00a0 -152\u00a0 \u00a0<\/span><br \/>\n456<\/p>\n<p class=\"p1\">Next, we multiply 6 and 76 and write that product underneath<br \/>\nthe 456 and subtract:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-52480\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-93.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-93\" width=\"133\" height=\"158\" \/><br \/>\nWe are left with no remainder and a final quotient of 2.6.<\/p>\n<p><strong>2.7 Lesson<\/strong><\/p>\n<p><strong>Key Idea<\/strong><br \/>\nDividing Decimals by Whole Numbers<br \/>\n<strong>Words<\/strong><br \/>\nPlace the decimal point in the quotient above the decimal point in the dividend.<br \/>\nThen divide as you would with whole numbers. Continue until there is no remainder.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27365\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-296.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 296\" width=\"416\" height=\"83\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-296.png 416w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-296-300x60.png 300w\" sizes=\"(max-width: 416px) 100vw, 416px\" \/><\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Divide. Use estimation to check your answer.<\/strong><\/p>\n<p>Question 1.<br \/>\n36.4 \u00f7 2<br \/>\n36.4 \u00f7 2 = 18.2<br \/>\nEstimation is reasonable,<\/p>\n<p>Explanation:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-52486\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-94.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-94\" width=\"288\" height=\"251\" \/><br \/>\nTherefore, 36.4 \u00f7 2 = 18.2,<br \/>\nEstimation is 36 \u00f7 2 = 18 is reasonable.<\/p>\n<p>Question 2.<br \/>\n22.2 \u00f7 6<br \/>\n22.2 \u00f7 6 = 3.7,<br \/>\nEstimation is reasonable,<\/p>\n<p>Explanation:<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 3.7\u00a0<\/span><br \/>\n6)22.2\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a06 X 3 = 18<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a018\u00a0 \u00a0\u00a0<\/span><br \/>\n4.2\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a06 X 0.7 = 4.2<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a04.2<\/span><br \/>\n0<br \/>\nTherefore,\u00a0 22.2 \u00f7 6 = 3.7.<br \/>\nEstimation is 22 \u00f7 6 = 3.66 is reasonale.<\/p>\n<p>Question 3.<br \/>\n59.64 \u00f7 7<br \/>\n59.64 \u00f7 7 = 8.52,<br \/>\nEstimation is reasonable,<\/p>\n<p>Explanation:<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 8.52\u00a0\u00a0<\/span><br \/>\n7)59.64\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 7 X 8 = 56<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a056\u00a0 \u00a0\u00a0<\/span><br \/>\n3.6\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a07 X 0.5 = 3.5<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a03.5\u00a0 \u00a0<\/span><br \/>\n0.14\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 7 X 0.02 = 0.14<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a00.14<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a00<br \/>\nTherefore,\u00a0 59.64 \u00f7 7 = 8.52,<br \/>\nEstimation is 60 \u00f7 7 = 8.57 is reasonale.<\/p>\n<p>Question 4.<br \/>\n3.12 \u00f7 16<br \/>\n3.12 \u00f7 16 = 0.195,<br \/>\nEstimation is reasonable,<\/p>\n<p>Explanation:<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 0.195<\/span><br \/>\n16)3.12\u00a0 \u00a0 \u00a0 \u00a0 \u00a016 X 0.1 = 1.6<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a01.6<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 1.52\u00a0 \u00a0 \u00a0 \u00a0 16 X 0.09 = 1.44<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 1.44<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 0.08\u00a0 \u00a0 \u00a0 \u00a0 16 X 0.005 = 0.08<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a00.08<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a00<br \/>\nTherefore, 3.12 \u00f7 16 = 0.195,<br \/>\nEstimation is 3 \u00f7 16 = 0.187 is reasonale.<\/p>\n<p>Question 5.<br \/>\n6.224 \u00f7 4<br \/>\n6.224 \u00f7 4 = 1.556,<br \/>\nEstimation is reasonable,<\/p>\n<p>Explanation:<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 1.556<\/span><br \/>\n4)6.224\u00a0 \u00a0 \u00a0 \u00a0 \u00a04 X 1 = 4<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a04<br \/>\n<\/span>\u00a0 \u00a0 2\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a04 X 0.5 =2<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 2\u00a0 \u00a0 <\/span><br \/>\n0.2\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a04 X 0.05 = 0.2\u00a0 \u00a0 \u00a0\u00a0<span style=\"text-decoration: underline;\"><br \/>\n0.2<br \/>\n<\/span>\u00a0 \u00a0 0.024\u00a0 \u00a0 \u00a0 \u00a04 X 0.006 = 0.024<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 0.024<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a00<span style=\"text-decoration: underline;\"><br \/>\n<\/span>Therefore, 6.224 \u00f7 4 = 1.556,<br \/>\nEstimation is 6 \u00f7 4 = 1.5 is reasonale.<\/p>\n<p>Question 6.<br \/>\n43.407 \u00f7 14<br \/>\n43.407 \u00f7 14 = 3.1005,<br \/>\nEstimation is reasonable,<\/p>\n<p>Explanation:<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 3.1005\u00a0<\/span><br \/>\n14)43.407\u00a0 \u00a0 \u00a0 \u00a0 14 X 3 = 42<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a042<br \/>\n<\/span>\u00a0 \u00a0 \u00a01.4\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a014 X 0.1 = 1.4<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a01.4\u00a0 \u00a0 <\/span><br \/>\n0.007\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 14 X 0.0005 = 0.007\u00a0 \u00a0 \u00a0\u00a0<span style=\"text-decoration: underline;\"><br \/>\n0.007<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 0<br \/>\nTherefore, 43.407 \u00f7 14 = 3.1005,<br \/>\nEstimation is 43 \u00f7 14 = 3.0714 is reasonale.<\/p>\n<p><strong>Key Idea<\/strong><\/p>\n<p><strong>Dividing Decimals by Decimals<br \/>\n<\/strong><strong>Words<\/strong><br \/>\nMultiply the divisor and the dividend by a power of 10 to make<br \/>\nthe divisor a whole number. Then place the decimal point in the<br \/>\nquotient above the decimal point in the dividend and divide as<br \/>\nyou would with whole numbers. Continue until there is no remainder.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27366\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-297.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 297\" width=\"508\" height=\"137\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-297.png 508w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-297-300x81.png 300w\" sizes=\"(max-width: 508px) 100vw, 508px\" \/><\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Divide. Check your answer.<\/strong><\/p>\n<p>Question 7.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27367\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-298.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 298\" width=\"69\" height=\"36\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27367\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-298.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 298\" width=\"69\" height=\"36\" \/> = 8<\/p>\n<p>Explanation:<br \/>\nGiven expression is 9.6 \u00f7 1.2 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 8\u00a0 \u00a0 \u00a0<\/span><br \/>\n1.2) 9.6\u00a0 \u00a0 \u00a0 1.2 X 8 = 9.6<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a09.6<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 0<br \/>\nTherefore, 9.6 \u00f7 1.2 = 9.6.<\/p>\n<p>Question 8.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27368\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-299.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 299\" width=\"66\" height=\"38\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27368\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-299.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 299\" width=\"66\" height=\"38\" \/>= 17<br \/>\nExplanation:<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 17\u00a0 \u00a0 \u00a0 \u00a0\u00a0<\/span><br \/>\n3.4)57.8\u00a0 \u00a0 \u00a0 \u00a0 3.4 X 17 = 57.8<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 57.8<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 0<br \/>\nTherefore, 57.8 \u00f7 3.4 = 17.<\/p>\n<p>Question 9.<br \/>\n21.643 \u00f7 2.3<br \/>\n21.643 \u00f7 2.3 = 9.41<\/p>\n<p>Explanation:<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 9.41\u00a0 \u00a0\u00a0<\/span><br \/>\n2.3)21.643\u00a0 \u00a0 \u00a0 2.3 X 9 = 20.7<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 20.7<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 0.94\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 2.3 X 0.4 = 0.92<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 0.92\u00a0 \u00a0 \u00a0<\/span><br \/>\n0.023\u00a0 \u00a0 \u00a0 \u00a0 \u00a02.3 X 0.01 = 0.023\u00a0 \u00a0 \u00a0\u00a0<span style=\"text-decoration: underline;\"><br \/>\n0.023<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 0<br \/>\nTherefore, 21.643 \u00f7 2.3 = 9.41.<\/p>\n<p>Question 10.<br \/>\n0.459 \u00f7 0.51<br \/>\n0.459 \u00f7 0.51 =0.9<\/p>\n<p>Explanation:<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 0.9\u00a0 \u00a0\u00a0<\/span><br \/>\n0.51)0.459\u00a0 \u00a0 \u00a0 0.51 X 0.9 = 0.459<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 0.459<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 0<\/p>\n<p>Therefore, 0.51 \u00f7 0.9 = 0.459<\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Divide. Check your answer.<\/strong><\/p>\n<p>Question 11.<br \/>\n3.8 \u00f7 0.16<br \/>\n3.8 \u00f7 0.16 = 23.75<\/p>\n<p>Explanation:<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 23.75\u00a0 \u00a0\u00a0<\/span><br \/>\n0.16)3.8\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 0.16 X 23 = 3.68<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 3.68<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 0.120\u00a0 \u00a0 \u00a0 0.16 X 0.7 = 0.112<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 0.112\u00a0 \u00a0 \u00a0<\/span><br \/>\n0.008\u00a0 \u00a0 \u00a0 \u00a0 0.16 X 0.05 = 0.008\u00a0 \u00a0 \u00a0\u00a0<span style=\"text-decoration: underline;\"><br \/>\n0.008<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 0<br \/>\nTherefore, 3.8 \u00f7 0.16 = 23.75.<\/p>\n<p>Question 12.<br \/>\n15.6 \u00f7 0.78<br \/>\n15.6 \u00f7 0.78 = 20<\/p>\n<p>Explanation:<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 20\u00a0 \u00a0\u00a0<\/span><br \/>\n0.78)15.6\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 0.78 X 20 = 15.6<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 15.6<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 0<br \/>\nTherefore, 15.6 \u00f7 0.78 = 20.<\/p>\n<p>Question 13.<br \/>\n7.2 \u00f7 0.048<br \/>\n7.2 \u00f7 0.048 = 150<\/p>\n<p>Explanation:<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0150\u00a0 \u00a0\u00a0<\/span><br \/>\n0.048)7.2\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 0.048 X 150 = 7.2<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a07.2<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 0<br \/>\nTherefore, 7.2 \u00f7 0.048 = 7.2.<\/p>\n<p>Question 14.<br \/>\n42 \u00f7 3.75<br \/>\n42 \u00f7 3.75 = 11.2<\/p>\n<p>Explanation:<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 11.2\u00a0 \u00a0\u00a0<\/span><br \/>\n3.75) 42\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 3.75 X 11= 41.25<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a041.25<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 0.75\u00a0 \u00a0 \u00a0 \u00a0 3.75 X 0.2 = 0.75<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 0.75\u00a0 \u00a0 \u00a0<\/span><br \/>\n0<br \/>\nTherefore, 42 \u00f7 3.75 = 11.2.<\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><br \/>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p><strong>DIVIDING DECIMALS<\/strong><br \/>\n<strong>Divide. Check your answer.<\/strong><\/p>\n<p>Question 15.<br \/>\n37.7 \u00f7 13<br \/>\n37.7 \u00f7 13 = 2.9<\/p>\n<p>Explanation:<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a02.9\u00a0 \u00a0\u00a0<\/span><br \/>\n13)37.7\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 13 X 2 = 26<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a026<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a011.7\u00a0 \u00a0 \u00a0 \u00a0 13 X 0.9 = 11.7<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a011.7\u00a0 \u00a0\u00a0<\/span><br \/>\n0<br \/>\nTherefore, 37.7 \u00f7 13 = 2.9.<\/p>\n<p>Question 16.<br \/>\n33 \u00f7 4.4<br \/>\n33 \u00f7 4.4 = 7.5<\/p>\n<p>Explanation:<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a07.5\u00a0 \u00a0\u00a0<\/span><br \/>\n4.4)33\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a04.4 X 7 = 30.8<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 30.8<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 2.2\u00a0 \u00a0 \u00a0 \u00a0 4.4 X 0.5 = 2.2<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 2.2\u00a0 \u00a0\u00a0<\/span><br \/>\n0<br \/>\nTherefore, 33 \u00f7 4.4 = 7.5.<\/p>\n<p>Question 17.<br \/>\n2.16 \u00f7 0.009<br \/>\n2.16 \u00f7 0.009 = 240<\/p>\n<p>Explanation:<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0240\u00a0 \u00a0 \u00a0 \u00a0<\/span><br \/>\n0.009)2.16\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a00.009 X 240 = 2.16<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 2.16<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a00<br \/>\nTherefore, 33 \u00f7 4.4 = 7.5.<\/p>\n<p>Question 18.<br \/>\n<strong>NUMBER SENSE<\/strong><br \/>\nFix the one that is not correct.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27369\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-300.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 300\" width=\"310\" height=\"80\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-300.png 310w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-300-300x77.png 300w\" sizes=\"(max-width: 310px) 100vw, 310px\" \/><br \/>\nThe one is not correct,<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 6.1\u00a0 \u00a0<\/span><br \/>\n4)2.44<\/p>\n<p>Explanation:<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 0.61\u00a0\u00a0<\/span><br \/>\n4)2.44\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 4 X 0.61 = 2.44<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a02.44<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 0<br \/>\n2.44 \u00f74 = 0.61 \u2260 6.1<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 6.1\u00a0 \u00a0<\/span><br \/>\n4)2.44\u00a0 \u00a0 is the one which is incorrect.<\/p>\n<p>Question 19.<br \/>\n<strong>NUMBER SENSE<\/strong><br \/>\nRewrite <img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27371\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-301.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 2 Fractions and Decimals 301\" width=\"68\" height=\"34\" \/> so that the divisor is a whole number.<\/p>\n<p>18.5 \u00f7 2, Here the divisor is a whole number<\/p>\n<p>Explanation:<br \/>\nHere 2.16 is the divisor,<br \/>\nWe rewrite divisor as a whole number as 2.16 \u2248 2,<br \/>\n18.5 \u00f7 2.<\/p>\n<p>Question 20.<br \/>\n<strong>STRUCTURE<\/strong><br \/>\nWrite 1.8 \u00f7 6 as a multiplication problem with a missing factor.<br \/>\nExplain your reasoning.<\/p>\n<p>1.8 \u00f7 6 as a multiplication problem with a missing factor is<br \/>\n6 X _____ = 1.8<\/p>\n<p>Explanation:<br \/>\nGiven expression as 1.8 \u00f7 6 now we write as<br \/>\na multiplication problem as<br \/>\nwe know 1.8 \u00f7 6 = 0.3 means , So 1.8 = 6 X 0.3,<br \/>\nNow we write 1.8 = 6 X 0.3, with as missing factor as<br \/>\n6 X _____ = 1.8.<br \/>\nTherefore, 1.8 \u00f7 6 as a multiplication problem with a<br \/>\nmissing factor is 6 X _____ = 1.8.<\/p>\n<p><strong>Self-Assessment for Problem Solving<\/strong><\/p>\n<p>Solve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 21.<br \/>\nA magazine subscription costs $29.88 for 12 issues or $15.24 for 6 issues.<br \/>\nWhich subscription costs more per issue? How much more?<\/p>\n<p>$15.24 for 6 issues subscription costs more per issue and<br \/>\nmore it costs is $0.05,<\/p>\n<p>Explanation:<br \/>\nGiven a magazine subscription costs $29.88 for 12 issues,<br \/>\nmeans 1 issue it is $29.88 \u00f7 12 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a02.49\u00a0 \u00a0<\/span><br \/>\n12)29.88\u00a0 \u00a0 \u00a0 12 X 2.49 = 29.33<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a029.88<br \/>\n0<br \/>\n<\/span>So each issue it is $2.49,<br \/>\nNow we have $15.24 for 6 issues means for 1 issue it is<br \/>\n$15.24 \u00f7 6 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 2.54\u00a0 \u00a0<\/span><br \/>\n6)15.24\u00a0 \u00a0 \u00a0 6 X 2.54 = 15.24<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 15.24\u00a0 <\/span><br \/>\n0<br \/>\nSo each issue it is $2.54.<br \/>\nNow how much costs more is $2.54 minus $ 2.49 =<br \/>\n2.54<br \/>\n<span style=\"text-decoration: underline;\">-2.49<br \/>\n0.05<br \/>\n<\/span>Therefore, $15.24 for 6 issues subscription costs more per issue and<br \/>\nmore it costs is $0.05.<\/p>\n<p>Question 22.<br \/>\nThe track of a roller coaster is 1.265 miles long. The ride lasts for 2.3 minutes.<br \/>\nWhat is the average speed of the roller coaster in miles per hour?<\/p>\n<p>33 miles per hour is the average speed of the roller coaster,<\/p>\n<p>Explanation:<br \/>\nGiven the track of a roller coaster is 1.265 miles long.<br \/>\nThe ride lasts for 2.3 minutes.<br \/>\nNow the average speed of the roller coaster in miles per hour is<br \/>\nwe know speed = distance \u00f7 time = 1.265 \u00f7 2.3 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a00.55\u00a0 \u00a0\u00a0<\/span><br \/>\n2.3)1.265\u00a0 \u00a0 \u00a02.3 X 0.55 = 1.265<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 1.265<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 0<br \/>\nAs speed = 0.55 miles per minute we convert it into hours as<br \/>\n0.55 X 60 = 33 miles per hour.<br \/>\ntherefore, 33 miles per hour is the average speed of the roller coaster.<\/p>\n<p>Question 23.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nThe table shows the number of visitors to a website each year for 4 years.<br \/>\nDoes the number of visitors increase more from Year 1 to Year 2 or<br \/>\nfrom Year 3 to Year 4? How many times greater is the increase?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27372\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-302.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 2 Fractions and Decimals 302\" width=\"178\" height=\"180\" \/><br \/>\nYes, the number of visitors increased more from Year 1 to Year 2<br \/>\ncompared to Year 3 to Year 4,<br \/>\n2.1 times greater is the increase.<\/p>\n<p>Explanation:<br \/>\nGiven the table shows the number of visitors to a website<br \/>\neach year for 4 years,<br \/>\nthe number of visitors increase more from Year 1 to Year 2 is<br \/>\nYear 2 &#8211; 32.22 millions and Year 1- 2.4 millions,<br \/>\nincreased in more are 32.22 -2.4 =<br \/>\n32.22<br \/>\n<span style=\"text-decoration: underline;\">-2.4<\/span><br \/>\n<span style=\"text-decoration: underline;\">29.82 millions<\/span><br \/>\nNow the number of visitors increase more from Year 3 to Year 4 is<br \/>\nYear 4 &#8211; 102.6 millions and Year 3 &#8211; 88.4 millions<br \/>\nincreased in more are 102.6 &#8211; 88.4 =<br \/>\n102.6<br \/>\n<span style=\"text-decoration: underline;\">-88.4<br \/>\n14.2 millions<br \/>\n<\/span>The number of visitors increased more from Year 1 to Year 2 is when<br \/>\ncompared to Year 3 to Year 4 , by more times is 29.82 \u00f7 14.2 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a02.1\u00a0 \u00a0 \u00a0<\/span><br \/>\n14.2)29.82\u00a0 \u00a0 \u00a014.2 X 2 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 28.40<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 1.42\u00a0 \u00a0 \u00a014.2 X 0.1 = 1.42<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 1.42<br \/>\n0<br \/>\n<\/span>So it is 2.1 times greater in the increase from Year 1 to Year 2.<\/p>\n<h3>Dividing Decimals Homework &amp; Practice 2.7<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Divide.<\/strong><\/p>\n<p>Question 1.<br \/>\n84 \u00f7 14<br \/>\n84 \u00f7 14 = 6<\/p>\n<p>Explanation:<br \/>\nGiven expression as 84 \u00f7 14 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a06\u00a0 \u00a0\u00a0<\/span><br \/>\n14)84\u00a0 \u00a0 \u00a0 \u00a014 X 6 = 84<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a084<br \/>\n0<br \/>\n<\/span>Therefore, 84 \u00f7 14 = 6.<\/p>\n<p>Question 2.<br \/>\n391 \u00f7 23<br \/>\n391 \u00f7 23 = 17<\/p>\n<p>Explanation:<br \/>\nGiven expression as 391 \u00f7 23 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a017\u00a0 \u00a0\u00a0<\/span><br \/>\n23)391\u00a0 \u00a0 \u00a0 \u00a023 X 1 = 23<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a023<br \/>\n<\/span>\u00a0 \u00a0 \u00a0161\u00a0 \u00a0 \u00a0 \u00a023 X 7 = 161<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0161<br \/>\n0<br \/>\n<\/span>Therefore, 391 \u00f7 23 = 17.<\/p>\n<p>Question 3.<br \/>\n1458 \u00f7 54<br \/>\n1458 \u00f7 54 = 27<\/p>\n<p>Explanation:<br \/>\nGiven expression as 1458 \u00f7 54 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 27\u00a0 \u00a0\u00a0<\/span><br \/>\n54)1458\u00a0 \u00a0 \u00a0 \u00a054 X 2 = 108<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0108<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0378\u00a0 \u00a0 \u00a0 \u00a054 X 7 = 378<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0378<br \/>\n0<br \/>\n<\/span>Therefore, 1458 \u00f7 54 = 27.<\/p>\n<p>Question 4.<br \/>\n\\(\\frac{68,134}{163}\\)<br \/>\n\\(\\frac{68,134}{163}\\) = 418,<\/p>\n<p>Explanation:<br \/>\nGiven expression as \\(\\frac{68,134}{163}\\) =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 418\u00a0 \u00a0\u00a0<\/span><br \/>\n163)68134\u00a0 \u00a0 \u00a0 \u00a0 163 X 4 = 652<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0652<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0293\u00a0 \u00a0 \u00a0 \u00a0 \u00a0163 X 1 = 163<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0163<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a01304\u00a0 \u00a0 \u00a0 \u00a0163 X 8 = 1304<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 1304<br \/>\n0<br \/>\n<\/span>Therefore, \\(\\frac{68,134}{163}\\) = 418.<\/p>\n<p>Question 5.<br \/>\nWhat is the value of 18 + 3<sup>2<\/sup> \u00f7 [3 \u00d7 (8 \u2212 5)]?<br \/>\nA. 3<br \/>\nB. 19<br \/>\nC. 27<br \/>\nD. 49<\/p>\n<p>18 + 3<sup>2<\/sup> \u00f7 [3 \u00d7 (8 \u2212 5)] = 19, B,<\/p>\n<p>Explanation:<br \/>\nGiven 18 + 3<sup>2<\/sup> \u00f7 [3 \u00d7 (8 \u2212 5)] =<br \/>\n[3 X (8-5)] = 3 X 3 = 9<br \/>\n3<sup>2<\/sup> = 3 X 3 = 9,<br \/>\nNow 3<sup>2<\/sup> \u00f7 [3 \u00d7 (8 \u2212 5)] = 9 \u00f7 9 = 1<br \/>\nso, 18 + 1 = 19,<br \/>\ntherefore, 18 + 3<sup>2<\/sup> \u00f7 [3 \u00d7 (8 \u2212 5)] = 19, matches with B.<\/p>\n<p><strong>Add or subtract.<\/strong><\/p>\n<p>Question 6.<br \/>\n7.635 &#8211; 5.046<br \/>\n7.635 &#8211; 5.046 = 2.589<\/p>\n<p>Explanation:<br \/>\nGiven expression as 7.635 &#8211; 5.046 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 15,12,15<\/span><br \/>\n7.635<br \/>\n<span style=\"text-decoration: underline;\">-5.046<br \/>\n2.589<br \/>\n<\/span>therefore 7.635 &#8211; 5.046 = 2.589.<\/p>\n<p>Question 7.<br \/>\n12.177 + 3.09<br \/>\n12.177 + 3.09 = 15.267,<\/p>\n<p>Explanation:<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a01\u00a0\u00a0<\/span><br \/>\n12.177<br \/>\n<span style=\"text-decoration: underline;\">+ 3.090<br \/>\n15.267<br \/>\n<\/span>therefore 12.177 + 3.09 = 15.267.<\/p>\n<p>Question 8.<br \/>\n14.008 &#8211; 9.433<br \/>\n14.008 &#8211; 9.433 = 4.575,<\/p>\n<p>Explanation:<br \/>\n<span style=\"text-decoration: underline;\">\u00a014,9,10\u00a0<\/span><br \/>\n14.008<br \/>\n<span style=\"text-decoration: underline;\">&#8211; 9.433<br \/>\n4.575<br \/>\n<\/span>therefore 14.008 &#8211; 9.433 = 4.575.<\/p>\n<p><strong>Concepts, Skills, &amp; Problem Solving<\/strong><\/p>\n<p><strong>DIVIDING DECIMALS<\/strong><br \/>\n<strong>Write two division expressions represented by the area model. Then \ufb01nd the quotients. Explain how you found your answer.<\/strong> (See Exploration 1, p. 87.)<\/p>\n<p>Question 9.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27370\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-2-Fractions-and-Decimals-302.1.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals 302.1\" width=\"200\" height=\"191\" \/><\/p>\n<p>Two division expressions are \\(\\frac{54}{100}\\) \u00f7 \\(\\frac{6}{10}\\) =<br \/>\n\\(\\frac{9}{10}\\) or \\(\\frac{54}{100}\\)\u00a0 \u00f7 \\(\\frac{9}{10}\\) =<br \/>\n\\(\\frac{6}{10}\\), we rewrite\u00a0 the expression as<br \/>\n\\(\\frac{54}{10}\\) = \\(\\frac{6}{10}\\) X \\(\\frac{9}{10}\\),<\/p>\n<p>Explanation:<br \/>\nBy counting the blocks in the area model found<br \/>\nthe two division expressions are \\(\\frac{54}{100}\\) \u00f7 \\(\\frac{6}{10}\\)<br \/>\n= \\(\\frac{9}{10}\\)<br \/>\nIf we see the area model the purple color blocks show<br \/>\n54 out of 100 blocks.<br \/>\nnow we write as \\(\\frac{54}{100}\\) = \\(\\frac{6}{10}\\) X<br \/>\n\\(\\frac{9}{10}\\), So,\\(\\frac{54}{100}\\) = \\(\\frac{6 X 9}{10 X 10}\\).<\/p>\n<p>Question 10.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27373\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-303.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 2 Fractions and Decimals 303\" width=\"197\" height=\"194\" \/><br \/>\nTwo division expressions are \\(\\frac{16}{100}\\) \u00f7 \\(\\frac{2}{10}\\) =<br \/>\n\\(\\frac{8}{10}\\) or \\(\\frac{16}{100}\\)\u00a0 \u00f7 \\(\\frac{8}{10}\\) =<br \/>\n\\(\\frac{2}{10}\\), we rewrite\u00a0 the expression as<br \/>\n\\(\\frac{16}{100}\\) = \\(\\frac{8}{10}\\) X \\(\\frac{2}{10}\\),<br \/>\nSo \\(\\frac{16}{100}\\) = \\(\\frac{8 X 2}{10 X 10}\\).<\/p>\n<p>Explanation:<br \/>\nBy counting the blocks in the area model found<br \/>\nthe two division expressions are \\(\\frac{16}{100}\\) \u00f7 \\(\\frac{6}{10}\\)<br \/>\n= \\(\\frac{2}{10}\\) or \\(\\frac{16}{100}\\)\u00a0 \u00f7 \\(\\frac{8}{10}\\) =<br \/>\n\\(\\frac{2}{10}\\)<br \/>\nIf we see the area model the purple color blocks show<br \/>\n16 out of 100 blocks.<br \/>\nnow we write as \\(\\frac{16}{100}\\) = \\(\\frac{6}{10}\\) X<br \/>\n\\(\\frac{2}{10}\\), So,\\(\\frac{16}{100}\\) = \\(\\frac{6 X 2}{10 X 10}\\).<\/p>\n<p><strong>DIVIDING DECIMALS BY WHOLE NUMBERS<\/strong><br \/>\n<strong>Divide. Use estimation to check your answer.<\/strong><\/p>\n<p>Question 11.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27374\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-304.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 2 Fractions and Decimals 304\" width=\"60\" height=\"26\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27374\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-304.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 2 Fractions and Decimals 304\" width=\"60\" height=\"26\" \/>= 4.2<\/p>\n<p>Explanation:<br \/>\nGiven expression as 25.2 \u00f7 6<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 4.2\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0<\/span><br \/>\n6)25.2\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 6 X 4 = 24<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a024<br \/>\n<\/span>\u00a0 \u00a0 \u00a01.2\u00a0 \u00a0 \u00a0 \u00a0 \u00a06 X 0.2 = 1.2<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a01.2<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 0<br \/>\nTherefore 25.2 \u00f7 6 = 4.2.<\/p>\n<p>Question 12.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27375\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-305.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 2 Fractions and Decimals 305\" width=\"58\" height=\"34\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27375\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-305.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 2 Fractions and Decimals 305\" width=\"58\" height=\"34\" \/>= 6.7<\/p>\n<p>Explanation:<br \/>\nGiven expression as 33.5 \u00f7 5<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 6.7\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0<\/span><br \/>\n5)33.5\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 5 X 6 = 30<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a030<br \/>\n<\/span>\u00a0 \u00a0 \u00a03.5\u00a0 \u00a0 \u00a0 \u00a0 \u00a05 X 0.7 = 3.5<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a03.5<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 0<br \/>\nTherefore 33.5 \u00f7 5 = 6.7.<\/p>\n<p>Question 13.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27376\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-306.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 2 Fractions and Decimals 306\" width=\"54\" height=\"26\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27376\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-306.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 2 Fractions and Decimals 306\" width=\"54\" height=\"26\" \/> = 0.5<\/p>\n<p>Explanation:<br \/>\nGiven expression as 3.5 \u00f7 7<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 0.5\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0<\/span><br \/>\n7)3.5\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 7 X 0.5 = 3.5<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a03.5<br \/>\n<\/span>\u00a0 \u00a0 0<br \/>\nTherefore 3.5 \u00f7 7 = 0.5.<\/p>\n<p>Question 14.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27377\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-307.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 2 Fractions and Decimals 307\" width=\"64\" height=\"34\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27377\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-307.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 2 Fractions and Decimals 307\" width=\"64\" height=\"34\" \/>= 1.3<br \/>\nExplanation:<br \/>\nGiven expression as 3.5 \u00f7 7<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 0.5\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0<\/span><br \/>\n7)3.5\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 7 X 0.5 = 3.5<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a03.5<br \/>\n<\/span>\u00a0 \u00a0 0<br \/>\nTherefore 3.5 \u00f7 7 = 0.5.<\/p>\n<p>Question 15.<br \/>\n38.79 \u00f7 9<br \/>\n38.79 \u00f7 9 = 4.31<\/p>\n<p>Explanation:<br \/>\nGiven expression as\u00a0 38.79 \u00f7 9 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 4.31\u00a0 \u00a0\u00a0<\/span><br \/>\n9)38.79\u00a0 \u00a0 \u00a0 \u00a0 9 X 4 = 36<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a036<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a02.7\u00a0 \u00a0 \u00a0 \u00a0 9 X 0.3 = 2.7<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a02.7<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 0.09\u00a0 \u00a0 \u00a0 9 X 0.01 = 0.09<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 0.09<br \/>\n0<br \/>\n<\/span>Therefore, 38.79 \u00f7 9 = 4.31.<\/p>\n<p>Question 16.<br \/>\n37.72 \u00f7 4<br \/>\n37.72 \u00f7 4 = 9.43<\/p>\n<p>Explanation:<br \/>\nGiven expression as\u00a0 37.72 \u00f7 4 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a09.43\u00a0 \u00a0\u00a0<\/span><br \/>\n4)37.72\u00a0 \u00a0 \u00a0 \u00a0 4 X 9 = 36<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a036<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 1.7\u00a0 \u00a0 \u00a0 \u00a0 \u00a04 X 0.4 = 1.6<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 1.6<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 0.12\u00a0 \u00a0 \u00a04 X 0.03 = 0.12<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 0.12<br \/>\n0<br \/>\n<\/span>Therefore, 37.72 \u00f7 4 = 9.43.<\/p>\n<p>Question 17.<br \/>\n43.4 \u00f7 7<br \/>\n43.4 \u00f7 7 = 6.2<\/p>\n<p>Explanation:<br \/>\nGiven expression as\u00a0 43.4 \u00f7 7 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 6.2\u00a0 \u00a0\u00a0<\/span><br \/>\n7)43.4\u00a0 \u00a0 \u00a0 \u00a0 7 X 6 = 42<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a042<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 1.4\u00a0 \u00a0 \u00a0 \u00a0 7 X 0.2 = 1.4<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 1.4<br \/>\n<\/span><span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 0<br \/>\n<\/span>Therefore, 43.4 \u00f7 7 = 6.2.<\/p>\n<p>Question 18.<br \/>\n22.505 \u00f7 7<br \/>\n22.505 \u00f7 7 = 3.215<\/p>\n<p>Explanation:<br \/>\nGiven expression as\u00a0 22.505 \u00f7 7 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a03.215\u00a0 \u00a0\u00a0<\/span><br \/>\n7)22.505\u00a0 \u00a0 \u00a0 \u00a0 7 X 3 = 21<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a021<br \/>\n<\/span>\u00a0 \u00a0 \u00a01.5\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 7 X 0.2 = 1.4<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a01.4<br \/>\n<\/span>\u00a0 \u00a0 \u00a00.10\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 7 X 0.01 = 0.07<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a00.07<br \/>\n<\/span>\u00a0 \u00a0 \u00a00.035\u00a0 \u00a0 \u00a0 \u00a0 7 X 0.005 = 0.035<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a00.035<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 0\u00a0<span style=\"text-decoration: underline;\"><br \/>\n<\/span>Therefore, 22.505 \u00f7 7 = 3.215.<\/p>\n<p>Question 19.<br \/>\n44.64 \u00f7 8<br \/>\n44.64 \u00f7 8 = 5.58<\/p>\n<p>Explanation:<br \/>\nGiven expression as\u00a0 44.64 \u00f7 8 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a05.58\u00a0 \u00a0\u00a0<\/span><br \/>\n8)44.64\u00a0 \u00a0 \u00a0 \u00a0 8 X 5 = 40<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a040<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 4.6\u00a0 \u00a0 \u00a0 \u00a0 8 X 0.5 = 4.0<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 4.0<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 0.64\u00a0 \u00a0 \u00a0 8 X\u00a0 0.08 = 0.64<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 0.64<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 0<span style=\"text-decoration: underline;\"><br \/>\n<\/span>Therefore, 44.64 \u00f7 8 = 5.58.<\/p>\n<p>Question 20.<br \/>\n0.294 \u00f7 3<br \/>\n0.294 \u00f7 3 = 0.098<\/p>\n<p>Explanation:<br \/>\nGiven expression as 0.294 \u00f7 3 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a00.098\u00a0 \u00a0\u00a0<\/span><br \/>\n3)0.294\u00a0 \u00a0 \u00a0 \u00a0 3 X 0.09 = 0.27<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a00.27<br \/>\n<\/span>\u00a0 \u00a00.024\u00a0 \u00a0 \u00a0 \u00a0 3 X 0.008 = 0.024<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a00.024<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a00<span style=\"text-decoration: underline;\"><br \/>\n<\/span>Therefore, 0.294 \u00f7 3 = 0.098.<\/p>\n<p>Question 21.<br \/>\n3.6 \u00f7 24<br \/>\n3.6 \u00f7 24 = 0.15<\/p>\n<p>Explanation:<br \/>\nGiven expression as 3.6\u00f7 24 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a00.15\u00a0 \u00a0\u00a0<\/span><br \/>\n24)3.6\u00a0 \u00a0 \u00a0 \u00a0 24 X 0.1 = 2.16<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a02.4<br \/>\n<\/span>\u00a0 \u00a0 \u00a01.2\u00a0 \u00a0 \u00a0 \u00a024 X 0.05 = 1.2<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a01.2<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a00<span style=\"text-decoration: underline;\"><br \/>\n<\/span>Therefore, 3.6 \u00f7 24 = 0.15<\/p>\n<p>Question 22.<br \/>\n52.014 \u00f7 20<br \/>\n52.014 \u00f7 20 = 2.6007<\/p>\n<p>Explanation:<br \/>\nGiven expression as\u00a0 52.014 \u00f7 20 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 2.6007\u00a0 \u00a0\u00a0<\/span><br \/>\n20)52.014\u00a0 \u00a0 \u00a0 \u00a0 20 X 2 = 40<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a040<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 12\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 20X 0.6 = 12<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 12<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 0.014\u00a0 \u00a0 \u00a0 \u00a0 \u00a020 X\u00a0 0.0007 = 0.014<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 0.014<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 0<span style=\"text-decoration: underline;\"><br \/>\n<\/span>Therefore, 520.14 \u00f7 20 = 2.6007.<\/p>\n<p><strong>YOU BE THE TEACHER<\/strong><br \/>\n<strong>Your friend \ufb01nds the quotient. Is your friend correct? Explain your reasoning.<\/strong><\/p>\n<p>Question 23.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27378\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-308.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 2 Fractions and Decimals 308\" width=\"145\" height=\"192\" \/><\/p>\n<p>Yes, Friend is correct,<\/p>\n<p>Explanation:<br \/>\nGiven expression as\u00a0 28.08 \u00f7 9 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 3.12\u00a0\u00a0<\/span><br \/>\n9)28.08\u00a0 \u00a0 \u00a0 9 X 3 = 27<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a027<br \/>\n<\/span>\u00a0 \u00a0 \u00a01.0\u00a0 \u00a0 \u00a0 \u00a0 9 X 0.1 = 0.9<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a00.9<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 0.18\u00a0 \u00a0 \u00a0 \u00a09 X\u00a0 0.02 = 0.18<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 0.18<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 0<span style=\"text-decoration: underline;\"><br \/>\n<\/span>Therefore, 28.08 \u00f7 9 = 3.12,<br \/>\nwhich is same as friends findings,\u00a0 So friend is correct.<\/p>\n<p>Question 24.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27379\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-309.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 2 Fractions and Decimals 309\" width=\"139\" height=\"155\" \/><br \/>\nNo, Friend is incorrect,<\/p>\n<p>Explanation:<br \/>\nGiven expression as\u00a0 28.08 \u00f7 9 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 0.086\u00a0\u00a0<\/span><br \/>\n6)0.516\u00a0 \u00a0 \u00a0 6 X 0.08 = 0.48<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a00.48<br \/>\n<\/span>\u00a0 \u00a00.036\u00a0 \u00a0 \u00a0 \u00a06 X 0.006 = 0.036<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a00.036<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 0<span style=\"text-decoration: underline;\"><br \/>\n<\/span>Therefore, 0.516 \u00f7 6 = 0.086,<br \/>\nwhich is not same as friends findings of 0.86,<br \/>\nSo friend is incorrect.<\/p>\n<p>Question 25.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nYou buy the same pair of pants in 3 different colors for $89.85.<br \/>\nHow much does each pair of pants cost?<\/p>\n<p>Each pair of pants cost $29.95,<\/p>\n<p>Explanation:<br \/>\nGiven I buy the same pair of pants in 3 different colors for $89.85.<br \/>\nmeans cost is same, now each pair of pants cost $89.85 \u00f7 3 =<br \/>\n29.95<br \/>\n3)89.85\u00a0 \u00a0 3 X 2 = 6<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a06<br \/>\n<\/span>\u00a0 \u00a029\u00a0 \u00a0 \u00a0 \u00a0 3 X 9 = 27<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a027<br \/>\n<\/span>\u00a0 \u00a0 \u00a02.8\u00a0 \u00a0 \u00a03 X 0.9 = 2.7<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a02.7<\/span><br \/>\n0.15\u00a0 \u00a03 X 0.05 = 0.15<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a00.15<\/span><br \/>\n0<br \/>\ntherefore, each pair of pants cost $29.95.<\/p>\n<p>Question 26.<br \/>\n<strong>REASONING<\/strong><br \/>\nWhich pack of fruit punch is the best buy? Explain.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27380\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-310.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 2 Fractions and Decimals 310\" width=\"286\" height=\"173\" \/><\/p>\n<p>12 pack fruit punch is the best buy,<\/p>\n<p>Explanation:<br \/>\nGiven 4-pack is $2.95, 12 pack is $8.65 and 24 pack is $17.50,<br \/>\nnow we will see how much each pack will cost seperatley as<br \/>\ni. 4 pack &#8211; $2.95 means 2.95 \u00f7 4 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 0.7375<\/span><br \/>\n4)2.95\u00a0 \u00a0 \u00a0 4 X 0.7 = 2.8<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a02.8<\/span><br \/>\n0.15\u00a0 \u00a0 4 X 0.03 = 0.12<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 0.12<\/span><br \/>\n0.030\u00a0 \u00a04 X 0.007 = 0.028<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 0.028<\/span><br \/>\n0.002\u00a0 \u00a04 X 0.0005 = 0.002<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 0.002<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 0<br \/>\nSo if we take 4 pack it will cost for 1 pack as 0.7375,<br \/>\nii. 12 pack &#8211; $8.65 means 8.65 \u00f7 12 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 0.72082<\/span><br \/>\n12)8.65\u00a0 \u00a0 \u00a0 12 X 0.7 = 8.4<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a08.4<\/span><br \/>\n0.25\u00a0 \u00a0 \u00a0 \u00a012 X 0.02 = 0.24<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 0.24\u00a0 <\/span><br \/>\n0.01000\u00a0 \u00a012 X 0.0008 = 0.0096<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 0.00968<\/span><br \/>\n0.00032\u00a0 \u00a012 X 0.00002 = 0.00024<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 0.00024<br \/>\n<\/span>\u00a0 \u00a0 0.00008 remainder<br \/>\nSo if we take 12 pack it will cost for 1 pack as 0.72082,<br \/>\niii. 24 pack &#8211; $17.50 means 17.50 \u00f7 24 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 0.72916<\/span><br \/>\n24)17.50\u00a0 \u00a0 \u00a0 24 X 0.7 = 16.8<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a016.80<\/span><br \/>\n0.70\u00a0 \u00a0 \u00a0 24 X 0.02 = 0.48<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 0.48\u00a0 <\/span><br \/>\n0.220\u00a0 \u00a0 \u00a0 \u00a024 X 0.009 = 0.216<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 0.216<\/span><br \/>\n0.0040\u00a0 \u00a024 X 0.0001 = 0.0024<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 0.0024<br \/>\n<\/span>\u00a0 \u00a0 0.00160\u00a0 \u00a0 24 X 0.00006 = 0.001444<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 0.00144<br \/>\n<\/span>\u00a0 \u00a0 0.00016 remainder<br \/>\nSo if we take 24 pack it will cost for 1 pack as 0.72916,<br \/>\nNow we compare we get 0.72082&lt; 0.72916 &lt; 0.7375,<br \/>\ntherefore 12 pack fruit punch is the best buy.<\/p>\n<p><strong>DIVIDING DECIMALS<\/strong><br \/>\n<strong>Divide. Check your answer.<\/strong><\/p>\n<p>Question 27.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27381\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-311.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 2 Fractions and Decimals 311\" width=\"72\" height=\"31\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27381\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-311.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 2 Fractions and Decimals 311\" width=\"72\" height=\"31\" \/> = 12,<\/p>\n<p>Explanation:<br \/>\nGiven expression as\u00a0 25.2 \u00f7 2.1 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 12\u00a0\u00a0<\/span><br \/>\n2.1)25.2\u00a0 \u00a0 \u00a0 2.1 X 12 = 25.2<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a025.2<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a00<span style=\"text-decoration: underline;\"><br \/>\n<\/span>Therefore, 25.2 \u00f7 2.1 = 12.<\/p>\n<p>Question 28.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27382\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-312.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 2 Fractions and Decimals 312\" width=\"68\" height=\"38\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27382\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-312.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 2 Fractions and Decimals 312\" width=\"68\" height=\"38\" \/>= 9,<\/p>\n<p>Explanation:<br \/>\nGiven expression as\u00a0 34.2 \u00f7 3.8 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a09\u00a0 \u00a0 \u00a0<\/span><br \/>\n3.8)34.2\u00a0 \u00a0 \u00a0 3.8 X 9 = 34.2<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 34.2<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a00<span style=\"text-decoration: underline;\"><br \/>\n<\/span>Therefore, 34.2 \u00f7 3.8 = 9.<\/p>\n<p>Question 29.<br \/>\n36.47 \u00f7 0.7<br \/>\n36.47 \u00f7 0.7 = 52.1,<\/p>\n<p>Explanation:<br \/>\nGiven expression as\u00a0 36.47 \u00f7 0.7 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 52.1\u00a0 \u00a0 \u00a0<\/span><br \/>\n0.7)36.47\u00a0 \u00a0 \u00a0 0.7 X 52 = 36.4<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 36.4<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a00.07\u00a0 \u00a0 \u00a0 0.7 X 0.1 = 0.07<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a00.07<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 0<br \/>\nTherefore, 36.47 \u00f7 0.7 = 52.1.<\/p>\n<p>Question 30.<br \/>\n0.984 \u00f7 12.3<br \/>\n0.984 \u00f7 12.3 = 0.08,<\/p>\n<p>Explanation:<br \/>\nGiven expression as\u00a0 0.984 \u00f7 12.3 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 0.08\u00a0 \u00a0 \u00a0<\/span><br \/>\n12.3)0.984\u00a0 \u00a0 \u00a0 12.3 X 0.08\u00a0 = 0.984<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a00.984<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a00<br \/>\nTherefore, 0.984 \u00f7 12.3 = 0.08.<\/p>\n<p>Question 31.<br \/>\n6.64 \u00f7 8.3<br \/>\n6.64 \u00f7 8.3 = 0.8,<\/p>\n<p>Explanation:<br \/>\nGiven expression as\u00a0 6.64 \u00f7 8.3 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 0.8\u00a0 \u00a0 \u00a0<\/span><br \/>\n8.3)6.64\u00a0 \u00a0 \u00a0 8.3 X\u00a0 0.8 = 6.64<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a06.64<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 0<br \/>\nTherefore, 6.64 \u00f7 8.3 = 0.8.<\/p>\n<p>Question 32.<br \/>\n83.266 \u00f7 13.43<br \/>\n83.266 \u00f7 13.43 = 6.2,<\/p>\n<p>Explanation:<br \/>\nGiven expression as 83.266 \u00f7 13.43 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 6.2\u00a0 \u00a0 \u00a0 \u00a0\u00a0<\/span><br \/>\n13.43)83.266\u00a0 \u00a0 \u00a0 13.43 X 6 = 80.58<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 80.58<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a02.686\u00a0 \u00a0 \u00a0 \u00a013.43 X 0.2 = 2.686<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a02.686<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 0<br \/>\nTherefore, 83.266 \u00f7 13.43 = 6.2.<\/p>\n<p>Question 33.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27383\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-313.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 2 Fractions and Decimals 313\" width=\"86\" height=\"28\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27383\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-313.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 2 Fractions and Decimals 313\" width=\"86\" height=\"28\" \/>= 11.7,<\/p>\n<p>Explanation:<br \/>\nGiven expression as 1.053 \u00f7 0.09 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a011.7\u00a0 \u00a0 \u00a0 \u00a0\u00a0<\/span><br \/>\n0.09)1.053\u00a0 \u00a0 \u00a0 \u00a00.09 X 11 = 0.99<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 0.99<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 0.063\u00a0 \u00a0 \u00a0 \u00a00.09 X 0.7 = 0.063<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 0.063<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a00<br \/>\nTherefore, 1.053 \u00f7 0.09 = 11.7.<\/p>\n<p>Question 34.<br \/>\n35.903 \u00f7 16.1<br \/>\n35.903 \u00f7 16.1 = 2.23,<\/p>\n<p>Explanation:<br \/>\nGiven expression as 35.903 \u00f7 16.1 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 2.23\u00a0 \u00a0 \u00a0 \u00a0\u00a0<\/span><br \/>\n16.1)35.903\u00a0 \u00a0 \u00a0 \u00a016.1 X 2 = 32.2<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 32.2<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 3.70\u00a0 \u00a0 \u00a0 \u00a0 \u00a016.1 X 0.2 = 3.22<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 3.22<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a00.483\u00a0 \u00a0 \u00a0 \u00a0 16.1 X 0.03 = 0.483<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a00.483<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a00<br \/>\nTherefore, 35.903 \u00f7 16.1 = 2.23.<\/p>\n<p>Question 35.<br \/>\n0.996 \u00f7 0.12<br \/>\n0.996 \u00f7 0.12 = 8.3,<\/p>\n<p>Explanation:<br \/>\nGiven expression as 0.996 \u00f7 0.12 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 8.3\u00a0 \u00a0 \u00a0 \u00a0\u00a0<\/span><br \/>\n0.12)0.996\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 0.12 X 8 = 0.96<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 0.96<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 0.036\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 0.12 X 0.3 = 0.036<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 0.036<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 0<br \/>\nTherefore, 0.996 \u00f7 0.12 = 8.3.<\/p>\n<p>Question 36.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27384\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-314.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 2 Fractions and Decimals 314\" width=\"96\" height=\"36\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27384\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-314.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 2 Fractions and Decimals 314\" width=\"96\" height=\"36\" \/> = 2.7,<\/p>\n<p>Explanation:<br \/>\nGiven expression as 12.501 \u00f7 4.63 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 2.7\u00a0 \u00a0 \u00a0 \u00a0\u00a0<\/span><br \/>\n4.63)12.501\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 4.63 X 2 = 9.26<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 9.26<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 3.241\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 4.63 X 0.7 = 3.241<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 3.241<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a00<br \/>\nTherefore, 12.501 \u00f7 4.63 = 2.7.<\/p>\n<p>Question 37.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27385\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-315.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 2 Fractions and Decimals 315\" width=\"115\" height=\"33\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27385\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-315.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 2 Fractions and Decimals 315\" width=\"115\" height=\"33\" \/>= 0.23,<\/p>\n<p>Explanation:<br \/>\nGiven expression as 0.00115 \u00f7 0.005 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 0.23\u00a0 \u00a0 \u00a0 \u00a0\u00a0<\/span><br \/>\n0.005)0.00115\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 0.005 X 0.2 = 0.001<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 0.001<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 0.00015\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a00.005 X 0.03 = 0.00015<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 0.00015<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a00<br \/>\nTherefore, 0.00115 \u00f7 0.005 = 0.23.<\/p>\n<p>Question 38.<br \/>\n56.7175 \u00f7 4.63<br \/>\n56.7175 \u00f7 4.63 = 12.25,<\/p>\n<p>Explanation:<br \/>\nGiven expression as 56.7175 \u00f7 4.63 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 12.25\u00a0 \u00a0 \u00a0 \u00a0\u00a0<\/span><br \/>\n4.63)56.7175\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 4.63 X 12 = 55.56<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 55.56<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 1.1575\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 4.63 X 0.25 = 1.1575<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 1.1575<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a00<br \/>\nTherefore, 56.7175 \u00f7 4.63 = 12.25.<\/p>\n<p>Question 39.<br \/>\n4.23 \u00f7 0.012<br \/>\n4.23 \u00f7 0.012 = 352.5,<\/p>\n<p>Explanation:<br \/>\nGiven expression as 4.23 \u00f7 0.012 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 352.5\u00a0 \u00a0\u00a0<\/span><br \/>\n0.012)4.23\u00a0 \u00a0 \u00a0 \u00a0 0.012 X 352 = 4.224<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 4.224<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 0.006\u00a0 \u00a0 \u00a0 0.012 X 0.5 = 0.006<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 0.03<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a00<br \/>\nTherefore, 4.23 \u00f7 0.012 = 0.006.<\/p>\n<p>Question 40.<br \/>\n0.52 \u00f7 0.0013<br \/>\n0.52 \u00f7 0.0013 = 400,<\/p>\n<p>Explanation:<br \/>\nGiven expression as 0.52 \u00f7 0.0013 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0400\u00a0 \u00a0\u00a0<\/span><br \/>\n0.0013)0.52\u00a0 \u00a0 \u00a0 \u00a0 0.0013 X 400 = 0.52<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a00.52<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a00<br \/>\nTherefore, 0.52 \u00f7 0.0013 = 400.<\/p>\n<p>Question 41.<br \/>\n95.04 \u00f7 0.0132<br \/>\n95.04 \u00f7 0.0132 = 7,200,<\/p>\n<p>Explanation:<br \/>\nGiven expression as 95.04 \u00f7 0.0132 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a07200\u00a0 \u00a0\u00a0<\/span><br \/>\n0.0132)95.04\u00a0 \u00a0 \u00a0 \u00a0 0.0132 X 700 = 95.04<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 95.04<br \/>\n<\/span>\u00a0\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a00<br \/>\nTherefore, 95.04 \u00f7 0.0132 = 7,200.<\/p>\n<p>Question 42.<br \/>\n32.2 \u00f7 0.07<br \/>\n32.2 \u00f7 0.07 = 460,<\/p>\n<p>Explanation:<br \/>\nGiven expression as 32.2 \u00f7 0.07 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0460\u00a0 \u00a0 \u00a0\u00a0<\/span><br \/>\n0.07)32.2\u00a0 \u00a0 \u00a0 \u00a0 0.07 X 460 = 32.2<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 32.2<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 0<br \/>\nTherefore, 32.2 \u00f7 0.07 = 460.<\/p>\n<p>Question 43.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27386\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-316.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 2 Fractions and Decimals 316\" width=\"83\" height=\"32\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27386\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-316.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 2 Fractions and Decimals 316\" width=\"83\" height=\"32\" \/>= 40,<\/p>\n<p>Explanation:<br \/>\nGiven expression as 54.8 \u00f7 1.37 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a040\u00a0 \u00a0 \u00a0\u00a0<\/span><br \/>\n1.37)54.8\u00a0 \u00a0 \u00a0 \u00a0 1.37 X 40 = 54.8<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 54.8<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 0<br \/>\nTherefore, 54.8 \u00f7 1.37 = 40.<\/p>\n<p>Question 44.<br \/>\n44.2 \u00f7 3.25<br \/>\n44.2 \u00f7 3.25 = 13.6,<\/p>\n<p>Explanation:<br \/>\nGiven expression as 44.2 \u00f7 3.25 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 13.6\u00a0 \u00a0 \u00a0\u00a0<\/span><br \/>\n3.25)44.2\u00a0 \u00a0 \u00a0 \u00a0 3.25 X 13 = 42.25<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 42.25<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a01.95\u00a0 \u00a0 \u00a03.25 X 0.6 = 1.95<br \/>\nTherefore, 44.2 \u00f7 3.25 = 13.6.<\/p>\n<p>Question 45.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27387\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-317.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 2 Fractions and Decimals 317\" width=\"81\" height=\"34\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27387\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-317.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 2 Fractions and Decimals 317\" width=\"81\" height=\"34\" \/>= 12.5,<\/p>\n<p>Explanation:<br \/>\nGiven expression as 50.5 \u00f7 4.04 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 12.5\u00a0 \u00a0 \u00a0\u00a0<\/span><br \/>\n4.04)50.5\u00a0 \u00a0 \u00a0 \u00a0 4.04 X 12 = 48.48<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 48.48<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 2.02\u00a0 \u00a0 \u00a04.04 X 0.5 = 2.02<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 2.02<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 0<br \/>\nTherefore, 50.5 \u00f7 4.04 = 12.5.<\/p>\n<p>Question 46.<br \/>\n250 \u00f7 0.008<br \/>\n250 \u00f7 0.008 = 31250,<\/p>\n<p>Explanation:<br \/>\nGiven expression as 250 \u00f7 0.008 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a031250\u00a0 \u00a0 \u00a0\u00a0<\/span><br \/>\n0.008)250\u00a0 \u00a0 \u00a0 \u00a0 0.008 X 31250 = 250<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0250<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 0<br \/>\nTherefore, 250 \u00f7 0.008 = 31250.<\/p>\n<p>Question 47.<br \/>\n11.16 \u00f7 0.062<br \/>\n11.16 \u00f7 0.062 = 180,<\/p>\n<p>Explanation:<br \/>\nGiven expression as 11.16 \u00f7 0.062 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0180\u00a0 \u00a0 \u00a0<\/span><br \/>\n0.062)11.16\u00a0 \u00a0 \u00a0 \u00a0 0.062 X 180 = 11.16<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 11.16<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 0<br \/>\nTherefore, 11.16 \u00f7 0.062 = 180.<\/p>\n<p>Question 48.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27388\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-318.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 2 Fractions and Decimals 318\" width=\"73\" height=\"32\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27388\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-318.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 2 Fractions and Decimals 318\" width=\"73\" height=\"32\" \/>= 66.8,<\/p>\n<p>Explanation:<br \/>\nGiven expression as 835 \u00f7 12.5 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a066.8\u00a0 \u00a0 \u00a0\u00a0<\/span><br \/>\n12.5)835\u00a0 \u00a0 \u00a0 \u00a0 12.5 X 66 = 825<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 825<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 10\u00a0 \u00a0 \u00a0 \u00a012.5 X 0.8 = 10<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a010<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 0<br \/>\nTherefore, 835 \u00f7 12.5 = 66.8.<\/p>\n<p>Question 49.<br \/>\n597.6 \u00f7 12.45<br \/>\n597.6 \u00f7 12.45 = 48,<\/p>\n<p>Explanation:<br \/>\nGiven expression as 597.6 \u00f7 12.45 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 48\u00a0 \u00a0 \u00a0\u00a0<\/span><br \/>\n12.45)597.6\u00a0 \u00a0 \u00a0 \u00a0 12.45 X 48 = 597.6<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 597.6<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 0<br \/>\nTherefore, 597.6 \u00f7 12.45 = 48.<\/p>\n<p>Question 50.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27389\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-319.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 2 Fractions and Decimals 319\" width=\"107\" height=\"36\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27389\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-319.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 2 Fractions and Decimals 319\" width=\"107\" height=\"36\" \/> = 272,<\/p>\n<p>Explanation:<br \/>\nGiven expression as 118.32 \u00f7 0.435 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 272\u00a0 \u00a0 \u00a0\u00a0<\/span><br \/>\n0.435)118.32\u00a0 \u00a0 \u00a0 \u00a0 0.435 X 272 = 118.32<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 118.32<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 0<br \/>\nTherefore, 118.32 \u00f7 0.435 = 272.<\/p>\n<p>Question 51.<br \/>\n80.89 \u00f7 8.425<br \/>\n80.89 \u00f7 8.425 \u2248 9.60,<\/p>\n<p>Explanation:<\/p>\n<p>Explanation:<br \/>\nGiven expression as 80.89 \u00f7 8.425 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 9.60\u00a0 \u00a0 \u00a0\u00a0<\/span><br \/>\n8.425)80.89\u00a0 \u00a0 \u00a0 \u00a0 8.425 X 9 = 75.825<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 75.825<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 5.065\u00a0 \u00a0 \u00a08.425 X 0.6 = 5.055<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 5.055<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a00.010\u00a0 remainder<br \/>\nTherefore, 80.89 \u00f7 8.425 \u2248 9.60.<\/p>\n<p>Question 52.<br \/>\n0.8 \u00f7 0.6<br \/>\n0.8 \u00f7 0.6 \u2248 1.33,<\/p>\n<p>Explanation:<br \/>\nGiven expression as 0.8 \u00f7 0.6 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 1.33\u00a0 \u00a0<\/span><br \/>\n0.6)0.8\u00a0 \u00a0 \u00a0 \u00a0 0.6 X 1 = 75.825<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 0.6<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 0.20\u00a0 \u00a0 \u00a0 0.6 X 0.3 = 0.18<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 0.18<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 0.020\u00a0 \u00a0 0.6 X 0.03 = 0.018<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 0.018<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 0.002 \u00a0remainder<br \/>\nTherefore, 0.8 \u00f7 0.6 \u2248 1.33.<\/p>\n<p>Question 53.<br \/>\n38.9 \u00f7 6.44<br \/>\n38.9 \u00f7 6.44 = 6.04,<\/p>\n<p>Explanation:<br \/>\nGiven expression as 38.9 \u00f7 6.44 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 6.04\u00a0 \u00a0<\/span><br \/>\n6.44)38.9\u00a0 \u00a0 \u00a0 \u00a0 6.44 X 6 = 38.64<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 38.64<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 0.26\u00a0 \u00a0 \u00a0 6.44 X 0.04 = 0.2576<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 0.2576<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 0.0024\u00a0 remainder<br \/>\nTherefore, 38.9 \u00f7 6.44 = 6.04.<\/p>\n<p>Question 54.<br \/>\n11.6 \u00f7 0.95<br \/>\n11.6 \u00f7 0.95 = 12.2,<\/p>\n<p>Explanation:<br \/>\nGiven expression as 11.6 \u00f7 0.95 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 12.2\u00a0 \u00a0<\/span><br \/>\n0.95)11.6\u00a0 \u00a0 \u00a0 \u00a00.95 X 12 = 11.4<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 11.4<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 0.2\u00a0 \u00a0 \u00a0 0.95 X 0.2 = 0.19<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 0.19<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 0.01\u00a0 remainder<br \/>\nTherefore, 11.6 \u00f7 0.95 = 12.2.<\/p>\n<p>Question 55.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend rewrites the problem. Is your friend correct? Explain your reasoning.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27390\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-320.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 2 Fractions and Decimals 320\" width=\"256\" height=\"79\" \/><br \/>\nNo, Friend is incorrect, 146.4 \u00f7 0.32 \u2260 1.464 \u00f7 32,<br \/>\nWe rewrite as 1.464 \u00f7 32 as 14640 \u00f7 32,<\/p>\n<p>Explanation:<br \/>\nGiven 146.4 \u00f7 0.32 &#8212;&gt; 1.464 \u00f7 32,<br \/>\nfriend is incorrect as 146.4 \u00f7 0.32 = 146.4 X 100 by 32\u00a0 =<br \/>\n14640 by 32 \u2260 1.464 by 32, So friend is incorrect,<br \/>\nwe rewrite 1.464 \u00f7 32 as 14640 \u00f7 32 which is correct to<br \/>\n146.4 \u00f7 0.32 = 14640 \u00f7 32.<\/p>\n<p><strong>ORDER OF OPERATIONS<\/strong><br \/>\n<strong>Evaluate the expression.<\/strong><\/p>\n<p>Question 56.<br \/>\n7.68 + 3.18 \u00f7 12<br \/>\n7.68 + 3.18 \u00f7 12 = 7.945,<\/p>\n<p>Explanation:<br \/>\nGiven expression is 7.68 + 3.18 \u00f7 12,<br \/>\naccording to order of operations we take division first then<br \/>\naddition as 7.68 +(3.18 \u00f7 12) =<br \/>\nFirst we calculate 3.18 \u00f7 12 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a00.265<\/span><br \/>\n12)3.18\u00a0 \u00a0 12 X 0.2 = 2.4<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a02.4<br \/>\n<\/span>\u00a0 \u00a0 \u00a00.78\u00a0 \u00a0 \u00a0 12 X 0.06 = 0.72<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a00.72<br \/>\n<\/span>\u00a0 \u00a0 \u00a00.06\u00a0 \u00a0 12 X 0.005 = 0.06<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a00.06<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a00<br \/>\nWe got 3.18 \u00f7 12 = 0.265, Now we add 7.68 as<br \/>\n7.680<br \/>\n<span style=\"text-decoration: underline;\">+0.265<br \/>\n7.945<br \/>\n<\/span>therefore, 7.68 + 3.18 \u00f7 12 = 7.945.<\/p>\n<p>Question 57.<br \/>\n10.56 \u00f7 3 &#8211; 1.9<br \/>\n10.56 \u00f7 3 &#8211; 1.9 = 1.62,<\/p>\n<p>Explanation:<br \/>\nGiven expression is 10.56 \u00f7 3 &#8211; 1.9,<br \/>\naccording to order of operations we take division first then<br \/>\nsubtraction as\u00a0 (10.56 \u00f7 3) &#8211; 1.9 =<br \/>\nFirst we calculate 10.56 \u00f7 3 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 3.52\u00a0 \u00a0<\/span><br \/>\n3)10.56\u00a0 \u00a0 \u00a0 \u00a0 3 X 3 = 9<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a09.00<br \/>\n<\/span>\u00a0 \u00a0 \u00a01.5\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 3 X 0.5 = 1.5<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a01.5<br \/>\n<\/span>\u00a0 \u00a0 \u00a00.06\u00a0 \u00a0 \u00a0 \u00a0 3 X 0.02 = 0.06<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a00.06<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a00<br \/>\nWe got 10.56 \u00f7 3 = 3.52, Now we subtract 1.9 from 3.52 as<br \/>\n3.52<br \/>\n<span style=\"text-decoration: underline;\">-1.90<br \/>\n1.62<br \/>\n<\/span>therefore 10.56 \u00f7 3 &#8211; 1.9 = 1.62.<\/p>\n<p>Question 58.<br \/>\n19.6 \u00f7 7 \u00d7 9<br \/>\n19.6 \u00f7 7 X 9 = 25.2,<\/p>\n<p>Explanation:<br \/>\nGiven expression is 19.6 \u00f7 7 X 9,<br \/>\naccording to order of operations we take division first then<br \/>\nmultiplication as\u00a0 (19.6 \u00f7 7) X 9 =<br \/>\nFirst we calculate 19.6 \u00f7 7 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a02.8\u00a0 \u00a0<\/span><br \/>\n7)19.6\u00a0 \u00a0 \u00a0 \u00a07 X 2 = 14<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a014<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 5.6\u00a0 \u00a0 \u00a0 7 X 0.8 = 5.6<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 5.6<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 0<br \/>\nWe got 19.6 \u00f7 7 = 2.8, Now we multiply 2.8 with 9 as<br \/>\n<u>\u00a0 7\u00a0\u00a0<\/u><br \/>\n2.8\u00a0 &#8212;- 1 decimal place<span style=\"text-decoration: underline;\"><br \/>\nX 9<br \/>\n25.2 &#8212;- 1 decimal place<br \/>\n<\/span>therefore 19.6 \u00f7 7 X 9 = 25.2.<\/p>\n<p>Question 59.<br \/>\n5.5 \u00d7 16.56 \u00f7 9<br \/>\n5.5 \u00d7 16.56 \u00f7 9 = 10.12,<\/p>\n<p>Explanation:<br \/>\nGiven expression is 5.5 \u00d7 16.56 \u00f7 9<br \/>\naccording to order of operations we take multiplication first then<br \/>\ndivision as\u00a0 (5.5 X 16.56) \u00f7 9 =<br \/>\nFirst we calculate 5.5 X 16.56 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 2,2,3<\/span><br \/>\n<span style=\"text-decoration: underline;\">\u00a0 2,2,3<\/span><br \/>\n16.56 &#8212;- 2 decimal places<br \/>\n<span style=\"text-decoration: underline;\">X 5.5<br \/>\n<\/span>0828<br \/>\n<span style=\"text-decoration: underline;\">8280<br \/>\n91.08&#8212;- 2 decimal places<\/span><br \/>\nWe got 5.5 X 16.56 = 91.08, Now we divide 91.08 with 9 as<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a010.12<\/span><br \/>\n9)91.08\u00a0 \u00a0 \u00a09 X 10 = 90<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a090<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 1.0\u00a0 \u00a0 \u00a09 X 0.1 = 0.9<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 0.9<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 0.18\u00a0 \u00a0 9 X 0.02 = 0.18<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 0.18<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a00<br \/>\ntherefore 5.5 \u00d7 16.56 \u00f7 9 = 10.12.<\/p>\n<p>Question 60.<br \/>\n35.25 \u00f7 5 \u00f7 3<br \/>\n35.25 \u00f7 5 \u00f7 3 = 2.35,<\/p>\n<p>Explanation:<br \/>\nGiven expression is 35.25 \u00f7 5 \u00f7 3,<br \/>\naccording to order of operations we take division first then<br \/>\ndivision as\u00a0 (35.25 \u00f7 5) \u00f7 3 =<br \/>\nFirst we calculate 35.25 \u00f7 5 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 7.05<br \/>\n<\/span>5) 35.25\u00a0 \u00a0 \u00a0 5 X 7 = 35<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 35<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a00.25\u00a0 \u00a0 \u00a05 X 0.05 = 0.25<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a00.25<\/span><br \/>\n0<br \/>\nWe got 35.25 \u00f7 5 = 7.05, Now we divide 7.05 with 3 as<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a02.35<br \/>\n<\/span>3) 7.05\u00a0 \u00a0 \u00a0 3 X 2 = 6<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 6<br \/>\n<\/span>\u00a0 \u00a0 1.0\u00a0 \u00a0 \u00a0 \u00a0 3 X 0.3 = 0.9<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 0.9<br \/>\n<\/span>\u00a0 \u00a0 0.15\u00a0 \u00a0 \u00a03 X 0.05 = 0.15<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 0.15<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 0<br \/>\ntherefore,\u00a0 35.25 \u00f7 5 \u00f7 3 = 2.35.<\/p>\n<p>Question 61.<br \/>\n13.41 \u00d7 (5.4 \u00f7 9)<br \/>\n13.41 \u00d7 (5.4 \u00f7 9) = 8.046,<\/p>\n<p>Explanation:<br \/>\nGiven expression is 13.41 X (5.4 \u00f7 9),<br \/>\naccording to order of operations we take division first then<br \/>\nmultiplication so first we calculate 5.4 \u00f7 9 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a00.6\u00a0 \u00a0<\/span><br \/>\n9)5.4\u00a0 \u00a0 \u00a0 \u00a0 9 X 0.6 = 5.4<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a05.4\u00a0 \u00a0 <\/span><br \/>\n0<br \/>\nWe got 5.4 \u00f7 9 = 0.6, Now we multiply 13.41 with 0.6 as<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 1, 2\u00a0 \u00a0\u00a0<\/span><br \/>\n13.41&#8212;&#8212;2 decimal places<br \/>\n<span style=\"text-decoration: underline;\">X 0.6 &#8212;&#8211; 1 decimal place<br \/>\n8.046&#8212;&#8212;3 decimal places<br \/>\ntherefore, 13.41 \u00d7 (5.4 \u00f7 9) = 8.046.<\/span><\/p>\n<p>Question 62.<br \/>\n6.2 . (5.16 \u00f7 6.45)<br \/>\n6.2 X (5.16 \u00f7 6.45) = 4.96,<\/p>\n<p>Explanation:<br \/>\nGiven expression is 6.2 X (5.16 \u00f7 6.45),<br \/>\naccording to order of operations we take division first then<br \/>\nmultiplication so first we calculate 5.16 \u00f7 6.45 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a00.8\u00a0 \u00a0<\/span><br \/>\n6.45)5.16\u00a0 \u00a0 \u00a0 \u00a0 6.45 X 0.8 = 5.16<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 5.16\u00a0 \u00a0 <\/span><br \/>\n0<br \/>\nWe got 5.16 \u00f7 6.45 = 0.8, Now we multiply 6.2 with 0.8 as<br \/>\n<span style=\"text-decoration: underline;\">1<\/span><br \/>\n6.2 &#8212;- 1 decimal place<br \/>\n<span style=\"text-decoration: underline;\">X 0.8 &#8212;- 1 decimal place<br \/>\n<\/span>496<span style=\"text-decoration: underline;\"><br \/>\n000<br \/>\n4.96 &#8212;- 2 decimal places<br \/>\n<\/span>therefore, 6.2 X (5.16 \u00f7 6.45) = 4.96.<\/p>\n<p>Question 63.<br \/>\n132.06 \u00f7 (4<sup>2<\/sup> + 2.6)<br \/>\n132.06 \u00f7 (4<sup>2<\/sup> + 2.6) = 7.1,<\/p>\n<p>Explanation:<br \/>\nGiven expression as 132.06 \u00f7 (4<sup>2<\/sup> + 2.6) , first we calculate<br \/>\n(4<sup>2<\/sup> + 2.6) = 4 X 4 + 2.6 = 16 + 2.6 =<br \/>\n16<br \/>\n<span style=\"text-decoration: underline;\">+2.6<br \/>\n18.6<br \/>\n<\/span>Now, we divide 132.06 with 18.6 as<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 7.1\u00a0 \u00a0 \u00a0 \u00a0\u00a0<\/span><br \/>\n18.6)132.06\u00a0 \u00a018.6 X 7 = 130.2<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 130.2<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 1.86\u00a0 \u00a018.6 X 0.1 = 1.86<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 1.86<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a00<br \/>\ntherefore, 132.06 \u00f7 (4<sup>2<\/sup> + 2.6) = 7.1.<\/p>\n<p>Question 64.<br \/>\n4.8[23.9841 \u00f7 (1.16 + 1.27)]<br \/>\n4.8[23.9841 \u00f7 (1.16 + 1.27)] = 47.376,<\/p>\n<p>Explanation:<br \/>\nGiven expression as 4.8[23.9841 \u00f7 (1.16 + 1.27)],<br \/>\nfirst we calculate (1.16 + 1.27) =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 1\u00a0 \u00a0\u00a0<\/span><br \/>\n1.16<br \/>\n<span style=\"text-decoration: underline;\">+1.27<\/span><br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a02.43<br \/>\n<\/span>next we calculate 23.9841 \u00f7 2.43 as<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 9.87\u00a0 \u00a0 \u00a0\u00a0<\/span><br \/>\n2.43)23.9841\u00a0 \u00a0 \u00a02.43 X 9 = 21.87<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 21.87<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 2.114\u00a0 \u00a0 \u00a0 \u00a0 2.43 X 0.8 = 1.944<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 1.944<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 0.1701\u00a0 \u00a0 \u00a0 \u00a0 2.43 X 0.07 = 0.1701<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 0.1701<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a00<br \/>\nNow we multiply 4.8 with 9.87 as<br \/>\n9.87 &#8212;&#8211; 2 decimal places<br \/>\n<span style=\"text-decoration: underline;\">X4.8 &#8212;&#8211; 1 decimal place<br \/>\n<\/span>\u00a07.896<span style=\"text-decoration: underline;\"><br \/>\n39480<br \/>\n47.376&#8212;-3\u00a0decimal places<br \/>\n<\/span>therefore, 4.8[23.9841 \u00f7 (1.16 + 1.27)] = 47.376.<\/p>\n<p>Question 65.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nA person\u2019s running stride is about 1.14 times the person\u2019s height.<br \/>\nYour friend\u2019s stride is 5.472 feet. How tall is your friend?<\/p>\n<p>My friend is 4.8 feet tall,<\/p>\n<p>Explanation:<br \/>\nGiven a person\u2019s running stride is about 1.14 times the<br \/>\nperson\u2019s height. My friend\u2019s stride is 5.472 feet so my friend<br \/>\nheight is 5.472 \u00f7 1.14 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 4.8\u00a0 \u00a0 \u00a0<\/span><br \/>\n1.14)5.472\u00a0 \u00a0 \u00a01.14 X 4 = 4.56<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 4.56<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 0.912\u00a0 \u00a0 \u00a01.14 X 0.8 = 0.912<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 0.912<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 0<br \/>\ntherefore, my friend is 4.8 feet tall.<\/p>\n<p>Question 66.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nYou have 3.4 gigabytes available on your tablet.<br \/>\nA song is about 0.004 giga byte. How many songs can<br \/>\nyou download onto your tablet?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27391\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-321.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 2 Fractions and Decimals 321\" width=\"286\" height=\"186\" \/><\/p>\n<p>I can download 850 songs onto my tablet,<\/p>\n<p>Explanation:<br \/>\nGiven I have 3.4 gigabytes available on my tablet.<br \/>\nA song is about 0.004 giga byte. I can download<br \/>\n3.4 \u00f7 0.004 songs as<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 850\u00a0\u00a0<\/span><br \/>\n0.004)3.4\u00a0 \u00a0 0.004 X 850 = 3.4<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 3.4<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 0<br \/>\nTherefore, I can download 850 songs onto my tablet.<\/p>\n<p><strong>REASONING<\/strong><br \/>\n<strong>Without \ufb01nding the quotient, copy and complete the<br \/>\nstatement using &lt;, &gt;, or =. Explain your reasoning.<\/strong><\/p>\n<p>Question 67.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27392\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-322.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 2 Fractions and Decimals 322\" width=\"189\" height=\"35\" \/><br \/>\n6.66 \u00f7 0.74 = 66.6 \u00f7 7.4,<\/p>\n<p>Explanation:<br \/>\nGiven expressions as 6.66 \u00f7 0.74 , 66.6 \u00f7 7.4, now<br \/>\nwe write 66.6 \u00f7 7.4 as 6.66 X 10 \u00f7 7.4 = 6.66 \u00f7 0.74<br \/>\nnow both sides are equal, therefore<br \/>\n6.66 \u00f7 0.74 = 66.6 \u00f7 7.4.<\/p>\n<p>Question 68.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27393\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-323.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 2 Fractions and Decimals 323\" width=\"171\" height=\"42\" \/><br \/>\n32.2 \u00f7 0.7 &gt; 3.22 \u00f7 7,<\/p>\n<p>Explanation:<br \/>\nGiven expressions as 32.2 \u00f7 0.7,\u00a0 3.22 \u00f7 7,<br \/>\nnow 32.2 \u00f7 0.7 we write as 32.2 X 10 \u00f7 7 = 32.2 \u00f7 7,<br \/>\nnow we compare 32.2 \u00f7 7 and 3.22 \u00f7 7 if we see 32.2<br \/>\nis greater than 3.22 and both are divided by 7 only,<br \/>\nthe quotient of 32.2 will be greater than that of 3.22,<br \/>\nSo 32.2 \u00f7 0.7 &gt; 3.22 \u00f7 7.<\/p>\n<p>Question 69.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27394\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-324.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 2 Fractions and Decimals 324\" width=\"227\" height=\"40\" \/><br \/>\n160.72 \u00f7 16.4 &lt; 160.72 \u00f7 1.64 ,<\/p>\n<p>Explanation:<br \/>\nGiven expressions as 160.72 \u00f7 16.4 ,160.72 \u00f7 1.64 ,<br \/>\nif we compare we have 160.72 \u00f7 1.64 we can write as<br \/>\n160.72 X 10 \u00f7 1.64 X 10 = 1607.2 \u00f7 16.4 now if we compare<br \/>\n1607.2 is more than 160.72 and both are divided by 16.4,<br \/>\nSo 160.72 \u00f7 16.4 &lt; 160.72 \u00f7 1.64<\/p>\n<p>Question 70.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27395\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-325.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 2 Fractions and Decimals 325\" width=\"191\" height=\"39\" \/><br \/>\n75.6 \u00f7 63 &lt; 7.56 \u00f7 0.63,<\/p>\n<p>Explanation:<br \/>\nGiven expressions as 75.6 \u00f7 63 , 7.56 \u00f7 0.63 ,<br \/>\nif we compare we have 75.6 \u00f7 63 we can write as<br \/>\n0.756 X 100 \u00f7 0.63 X 100 = 0.756 \u00f7 0.63 now if we compare<br \/>\n7.56 is more than 0.756 and both are divided by 0.63,<br \/>\nSo 75.6 \u00f7 63 &lt; 7.56 \u00f7 0.63.<\/p>\n<p>Question 71.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nThe table shows the top three times in a swimming event at the Summer Olympics.<br \/>\nThe event consists of a team of four women swimming 100 meters each.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27396\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-326.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 2 Fractions and Decimals 326\" width=\"335\" height=\"174\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-326.png 335w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-326-300x156.png 300w\" sizes=\"(max-width: 335px) 100vw, 335px\" \/><br \/>\na. Suppose the times of all four swimmers on each team were the same.<br \/>\nFor each team, how much time does it take a swimmer to swim 100 meters?<br \/>\nb. Suppose each U.S. swimmer completed 100 meters a quarter second faster.<br \/>\nWould the U.S. team have won the gold medal? Explain your reasoning.<\/p>\n<p>a. For each team the time it will take a swimmer to<br \/>\nswim 100 meters is, for Australia it will be 52.6625 seconds,<br \/>\nfor United states it will be 52.9725 seconds and<br \/>\nfor Canada it will be 53.2225 seconds.<br \/>\nb. No, because even if U.S swimmer completes a quarter second faster<br \/>\nit becomes 210.89 which is more time than Australia team, So U.S team<br \/>\nwould not have won the gold medal.<\/p>\n<p>Explanation:<br \/>\nGiven table shows the top three times in a swimming event<br \/>\nat the Summer Olympics.<br \/>\na. For each team the time it will take a swimmer to<br \/>\nswim 100 meters is for Australia it will be 210.65 \u00f7 4 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a052.6625\u00a0<\/span><br \/>\n4)210.65\u00a0 \u00a0 \u00a0 4 X 5 = 20<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a020<br \/>\n<\/span>\u00a0 \u00a0 10\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a04 X 2 = 8<span style=\"text-decoration: underline;\"><br \/>\n8<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a02.6\u00a0 \u00a0 \u00a0 \u00a04 X 0.6 = 2.4<span style=\"text-decoration: underline;\"><br \/>\n2.4<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a00.25\u00a0 \u00a0 \u00a04 X 0.06 = 0.24<span style=\"text-decoration: underline;\"><br \/>\n0.24<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 0.010\u00a0 \u00a0 4 X 0.002 = 0.008<span style=\"text-decoration: underline;\"><br \/>\n0.008<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 0.002\u00a0 \u00a0 4 X 0.0005 = 0.002\u00a0<span style=\"text-decoration: underline;\"><br \/>\n0.002<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a00<br \/>\nfor Australia it will be 52.6625 seconds,<br \/>\nNow for United States 211.89 \u00f7 4 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a052.9725\u00a0<\/span><br \/>\n4)211.89\u00a0 \u00a0 \u00a0 4 X 5 = 20<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a020<br \/>\n<\/span>\u00a0 \u00a0 11\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a04 X 2 = 8<span style=\"text-decoration: underline;\"><br \/>\n08<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a03.8\u00a0 \u00a0 \u00a0 \u00a04 X 0.9 = 3.6<span style=\"text-decoration: underline;\"><br \/>\n3.6<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a00.29\u00a0 \u00a0 \u00a04 X 0.07 = 0.28<span style=\"text-decoration: underline;\"><br \/>\n0.28<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a00.010\u00a0 \u00a0 4 X 0.002 = 0.008<span style=\"text-decoration: underline;\"><br \/>\n0.008<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 0.002\u00a0 \u00a0 4 X 0.0005 = 0.002\u00a0<span style=\"text-decoration: underline;\"><br \/>\n0.002<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a00<br \/>\nfor United States it will be 52.9725 seconds,<br \/>\nNow for Canada it will be 212.89 \u00f7 4 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a053.2225\u00a0\u00a0<\/span><br \/>\n4)212.89\u00a0 \u00a0 \u00a0 4 X 5 = 20<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a020<br \/>\n<\/span>\u00a0 \u00a0 \u00a012\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a04 X 3 = 12<span style=\"text-decoration: underline;\"><br \/>\n12<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a00.8\u00a0 \u00a0 \u00a0 \u00a04 X 0.2 = 0.8<span style=\"text-decoration: underline;\"><br \/>\n0.8<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a00.09\u00a0 \u00a0 \u00a04 X 0.02 = 0.08<span style=\"text-decoration: underline;\"><br \/>\n0.08<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 0.010\u00a0 \u00a0 4 X 0.002 = 0.008<span style=\"text-decoration: underline;\"><br \/>\n0.008<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 0.002\u00a0 \u00a0 4 X 0.0005 = 0.002\u00a0<span style=\"text-decoration: underline;\"><br \/>\n0.002<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a00<br \/>\nfor Canada it will be 53.2225 seconds,<\/p>\n<p>b. If each U.S. swimmer completed 100 meters a quarter second faster,<br \/>\nwe will see the U.S. team have won the gold medal or not as<br \/>\nquarter second faster 4 women in each team means 1 second,<br \/>\nso it would have finished in 211.89 &#8211; 1 =<br \/>\n211.89<br \/>\n<span style=\"text-decoration: underline;\">&#8211;\u00a0 \u00a01.00<br \/>\n210.89<br \/>\n<\/span>Now comparing with Australia it will be 210.65 even then it is<br \/>\n210.89<br \/>\n<span style=\"text-decoration: underline;\">-210.65<br \/>\n0.24<br \/>\n<\/span>So U.S team would have taken 0.24 seconds more,<br \/>\ntherefore U.S team would not have won the gold medal.<\/p>\n<p>Question 72.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nTo approximate the number of bees in a hive, multiply the number<br \/>\nof bees that leave the hive in one minute by 3 and divide by 0.014.<br \/>\nYou count 25 bees leaving a hive in one minute. How many bees are in the hive?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27398\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-327.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 2 Fractions and Decimals 327\" width=\"695\" height=\"122\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-327.png 695w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-327-300x53.png 300w\" sizes=\"(max-width: 695px) 100vw, 695px\" \/>There are 5357 bees are in the hive,<\/p>\n<p>Explanation:<br \/>\nGiven to approximate the number of bees in a hive,<br \/>\nmultiply the number of bees that leave the hive in one<br \/>\nminute by 3 and divide by 0.014. I count 25 bees leaving<br \/>\na hive in one minutes so number of bees in the hive are<br \/>\n(25 X 3) \u00f7 0.014 = 75 \u00f7 0.014 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 5357<\/span><br \/>\n0.014)75.000\u00a0 \u00a0 \u00a00.014 X 5357 = 74.998<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 74.998<br \/>\n0.002\u00a0 remainder<br \/>\n<\/span>therefore there are 5357 bees are in the hive.<\/p>\n<p>Question 73.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nYou are saving money to buy a new bicycle that costs $155.75.<br \/>\nYou have $30 and plan to save $5 each week. Your aunt decides<br \/>\nto give you an additional $10 each week.<br \/>\na. How many weeks will you have to save until you<br \/>\nhave enough money to buy the bicycle?<br \/>\nb. How many more weeks would you have to save to<br \/>\nbuy a new bicycle that costs $203.89? Explain how you found your answer.<\/p>\n<p>a. 9 weeks I have to save until I have enough money to buy<br \/>\nthe bicycle.<br \/>\nb. 3 weeks more I have to save to buy a new bicycle that<br \/>\ncosts $203.89.<\/p>\n<p>Explanation:<br \/>\na. Given\u00a0 I am \u00a0saving money to buy a new bicycle that costs $155.75.<br \/>\nI have $30 and plan to save $5 each week. my aunt decides<br \/>\nto give me an additional $10 each week. So number of weeks<br \/>\nwill I have to save until I have enough money to buy the bicycle is,<br \/>\nI alreday have $30 means I need to save is\u00a0 $155.75 &#8211; $30 = $125.75,<br \/>\nevery week I can save $5 + $10 = $15,Now weeks it will take is<br \/>\n$125.75 \u00f7 15 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a08.383<\/span><br \/>\n15)125.75\u00a0 \u00a0 \u00a015 X 8 = 120<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0120<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 5.75\u00a0 \u00a0 15 X 0.3 = 4.5<span style=\"text-decoration: underline;\"><br \/>\n4.50<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a01.25\u00a0 \u00a015 X 0.08 = 1.20<span style=\"text-decoration: underline;\"><br \/>\n1.20<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a00.050\u00a0 \u00a015 X 0.003 = 0.045<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a00.045<\/span><br \/>\n0.0050\u00a0 \u00a0remainder<br \/>\ntherefore approximately I need to wait 9 weeks,<\/p>\n<p>b. Number of\u00a0more weeks would you have to save to<br \/>\nbuy a new bicycle that costs $203.89 , $\u00a0203.89 &#8211; $30 =<br \/>\n$173.89 I need to save, So number of weeks now is<br \/>\n$173.89 \u00f7 15 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a011.59\u00a0 \u00a0<\/span><br \/>\n15)173.89\u00a0 \u00a0 \u00a0 \u00a015 X 11 = 165<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0165<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a08.89\u00a0 \u00a0 \u00a0 \u00a015 X 0.5 = 7.5<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a07.50<\/span><br \/>\n1.39\u00a0 \u00a0 \u00a0 \u00a015 X 0.09 =1.35<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a01.35<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a00.04 remainder<br \/>\nTherefore approximately I need to wait 12 weeks,<br \/>\nSo more number of\u00a0 weeks would I have to save to<br \/>\nbuy a new bicycle that costs $203.89 is 3 weeks.<\/p>\n<p>Question 74.<br \/>\n<strong>PRECISION<\/strong><br \/>\nA store sells applesauce in two sizes.<br \/>\na. How many bowls of applesauce \ufb01t in a jar?<br \/>\nRound your answer to the nearest hundredth.<br \/>\nb. Explain two ways to \ufb01nd the better buy.<br \/>\nc. Which is the better buy?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27397\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-327.1.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 2 Fractions and Decimals 327.1\" width=\"193\" height=\"105\" \/><\/p>\n<p>a. Number of bowls of applesauce \ufb01t in a jar,<br \/>\nrounding answer to the nearest hundredth is 6.15.<br \/>\nb. i. First way is Dividing to find 1 ounce of applesauce<br \/>\nseperately,<br \/>\nii. Now we have unitary method,<br \/>\nc. The better buy is 24 ounce jar,<\/p>\n<p>Explanation:<br \/>\nGiven 3.9 ounce is bowl, So number of bowls of<br \/>\napplesauce fit in a jar is 24 \u00f7 3.9 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 6.153<\/span><br \/>\n3.9)24\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 3.9 X 6 = 23.4<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 23.4<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 0.6\u00a0 \u00a0 \u00a0 3.9 X 0.1 = 0.39<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 0.39<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 0.21\u00a0 \u00a0 3.9 X 0.05 = 0.195<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 0.195<\/span><br \/>\n0.015\u00a0 3.9 X 0.003 = 0.0117<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 0.011<br \/>\n0.004\u00a0 remainder<br \/>\n<\/span>therefore numberof bowls of applesauce \ufb01t in a jar,<br \/>\nrounding answer to the nearest hundredth is 6.15.<br \/>\nb. First way :<br \/>\n1 ounce bowl is $0.52 \u00f7 3.9<br \/>\n<span style=\"text-decoration: underline;\">0.133\u00a0 \u00a0\u00a0<\/span><br \/>\n3.9)0.52\u00a0 \u00a0 3.9 X 0.1 = 0.39<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 0.39<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 0.130\u00a0 \u00a03.9 X 0.03 = 0.117<span style=\"text-decoration: underline;\"><br \/>\n0.117<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 0.0130\u00a0 \u00a03.9 X 0.003 = 0.0117<span style=\"text-decoration: underline;\"><br \/>\n0.0117<br \/>\n0.0013\u00a0 remainder<br \/>\n<\/span>So 1 ounce bowl is $0.133<br \/>\nNow 1 ounce jar is $2.63 \u00f7 24<span style=\"text-decoration: underline;\"><br \/>\n0.109<br \/>\n<\/span>24)2.63\u00a0 \u00a0 \u00a0 24 X 0.1 = 2.4<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a02.4<br \/>\n<\/span>\u00a0 \u00a0 \u00a00.230\u00a0 \u00a0 \u00a0 24 X 0.009 = 0.216<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a00.216<br \/>\n0.014\u00a0 \u00a0remainder<\/span><\/p>\n<p>So 1 ounce jar is $0.109<br \/>\nSecond way :<br \/>\nWe know unitary methods we have 3.9 ounce bowl is $0.52,<br \/>\n24 once jar is $2.63 as both goes in 3 (3.9,24) we have<br \/>\n1 ounce bowl will be 3.9 \u00f7 3 = 0.52 \u00f7 3; 1.3 = 0.173,<br \/>\nNow 0.173 \u00f7 1.3 =<br \/>\n0.133<br \/>\n1.3)0.173\u00a0 \u00a01.3 X 0.133 = 0.1729<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 0.1729<br \/>\n0.0001 remainder<br \/>\n<\/span>So it is $0.1333 for 1 ounce bowl<br \/>\nNow 1 ounce jar is 24 \u00f7 3 = 2.63 \u00f7 3;\u00a0 8 = 0.876<br \/>\nNow 0.876 \u00f7 8 =<br \/>\n<span style=\"text-decoration: underline;\">0.1095<br \/>\n<\/span>8)0.876\u00a0 8 X 0.1095 = 0.876<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a00.876<br \/>\n<\/span>\u00a0 \u00a0 0<br \/>\nSo now 1 ounce jar is $0.1095,<br \/>\nC. We have 1 ounce bowl is $0.133 and 1 ounce jar is<br \/>\n$0.109, so on comparing $0.109&lt; $0.133\u00a0 jar is the better buy.<\/p>\n<p>Question 75.<br \/>\n<strong>GEOMETRY<\/strong><br \/>\nThe large rectangle\u2019s dimensions are three times the dimensions<br \/>\nof the small rectangle.<br \/>\na. How many times greater is the perimeter of the large rectangle than the<br \/>\nperimeter of the small rectangle?<\/p>\n<p>b. How many times greater is the area of the large rectangle than the<br \/>\narea of the small rectangle?<br \/>\nc. Are the answers to parts (a) and (b) the same? Explain why or why not.<br \/>\nd. What happens in parts (a) and (b) if the dimensions of the large rectangle<br \/>\nare two times the dimensions of the small rectangle?<br \/>\na. It will be 3 times greater is the perimeter of the large rectangle than the<br \/>\nperimeter of the small rectangle,<\/p>\n<p>b. It will be 9 times greater is the area of the large rectangle than the<br \/>\narea of the small rectangle.<\/p>\n<p>c. No, because perimeter will be measured in feet and<br \/>\narea is measured in\u00a0 square feet.<\/p>\n<p>d. Perimeter will be 2 times more in large rectangle and<br \/>\n4 times in area in large rectangle than the small rectangle.<\/p>\n<p>Explanation:<br \/>\nGiven the large rectangle\u2019s dimensions are three times the<br \/>\ndimensions of the small rectangle means lets take the<br \/>\nsmaller rectangle length as x and width y , Then the larger ones<br \/>\nwill be length 3x and width will be 3y,<br \/>\na. Now perimeter of both we know perimeter is<br \/>\nlength + breadth for smaller it will be (x+y) and for<br \/>\nlarger it will be 3x + 3y = 3(x + y), So It will be 3 times<br \/>\ngreater is the perimeter of the large rectangle than the<br \/>\nperimeter of the small rectangle.<br \/>\nb. Now we know area of rectangle is length X breadth,<br \/>\nwe have for small rectangle as x X y = xy and for large it<br \/>\nis 3x X 3y\u00a0 = 9xy which is 9 times greater is the area of the large<br \/>\nrectangle than the area of the small rectangle.<br \/>\nc. The answers are not the same in part a and part b,<br \/>\nbecause one will be measured in feet and other is square feet,<br \/>\n( one is adding and other is multiplying) both differs.<br \/>\nd. Now if the dimensions of the large rectangle<br \/>\nare two times the dimensions of the small rectangle<br \/>\nthen perimeter becomes as for small it is x + y and for<br \/>\nlarge it is 2x + 2y = 2(x + y) and area for small is xy and large<br \/>\n2x X 2y = 4xy, means perimeter will be 2 times more in large rectangle<br \/>\nand\u00a0 4 times in area in large rectangle than the small rectangle.<\/p>\n<h3>Fractions and Decimals Connecting Concepts<\/h3>\n<p><strong>2 Connecting Concepts<\/strong><\/p>\n<p><strong>Using the Problem-Solving Plan<\/strong><\/p>\n<p>Question 1.<br \/>\nYou change the water jug on the water cooler.<br \/>\nHow many glasses can be completely \ufb01lled before you need to<br \/>\nchange the water jug again?<br \/>\n<strong>Understand the problem<\/strong><br \/>\nYou know the capacities of the water jug and the glass.<br \/>\nYou are asked to determine how many glasses the water jug can \ufb01ll.<br \/>\n<strong>Make a plan.2<\/strong><br \/>\nFirst, use what you know about converting measures to<br \/>\n\ufb01nd the number of \ufb02uid ounces in 5 gallons. Then divide this amount<br \/>\nby the capacity of the glass to \ufb01nd the number of glasses that can be \ufb01lled.<br \/>\n<strong>Solve and check.<\/strong><br \/>\nUse the plan to solve the problem. Then check your solution.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27400\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-329.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 2 Fractions and Decimals 329\" width=\"190\" height=\"290\" \/><br \/>\n64 glasses can be completely \ufb01lled before we need to<br \/>\nchange the water jug again,<\/p>\n<p>Explanation:<br \/>\nWe know 1 gallons is equal to 128 fluid ounce,<br \/>\nSo in 5 gallons we have 5 X 128 = 640 fluid ounces water<br \/>\nis there in 5 gallons water jug.<br \/>\nNow we have 1 glass has 10 fluid ounces of water then in<br \/>\n640 it will be 640 \u00f7 10 = 64,<br \/>\ntherefore 64 glasses can be completely \ufb01lled before we need to<br \/>\nchange the water jug again.<\/p>\n<p>Question 2.<br \/>\nTwo ferries just departed from their docks at the same time.<br \/>\nFerry A departs from its dock every 1.2 hours. Ferry B departs<br \/>\nfrom its dock every 1.8 hours. How long will it be until both ferries<br \/>\ndepart from their docks at the same time again?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27401\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-330.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 2 Fractions and Decimals 330\" width=\"243\" height=\"185\" \/><\/p>\n<p>It will be at 3.6 hours until both ferries depart from their<br \/>\ndocks at the same time again.<\/p>\n<p>Explanation:<br \/>\nGiven two ferries just departed from their docks at the same time.<br \/>\nFerry A departs from its dock every 1.2 hours. Ferry B departs<br \/>\nfrom its dock every 1.8 hours. So the ratio is 1.2 : 1.8 = 2 : 3,<br \/>\nwe use cross product for equal hours, ratios as<br \/>\nboth meet at 1.2 X 3 = 3.6 hours or 1.8 X 2 = 3.6 hours,<br \/>\nSo,It will be at 3.6 hours until both ferries depart from their<br \/>\ndocks at the same time again.<\/p>\n<p>Question 3.<br \/>\nYou want to paint the ceiling of your bedroom. The ceiling has<br \/>\ntwo square skylights as shown. Each skylight has a side length of<br \/>\n1\\(\\frac{7}{8}\\) feet. How many square feet will you paint?<\/p>\n<p>Justify your answer.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27402\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-331.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 2 Fractions and Decimals 331\" width=\"195\" height=\"147\" \/><br \/>\nI will paint 132\\(\\frac{62}{64}\\) square feet,<\/p>\n<p>Explanation:<br \/>\nGiven\u00a0 the length and width of rectangle as<br \/>\n10 ft and 14 ft, Area of rectangle is length X breadth=<br \/>\n10 X 14 = 140 square feet,<br \/>\nNow we have 2 square sky light with 1\\(\\frac{7}{8}\\) feet,<br \/>\nso area of skylight is 1\\(\\frac{7}{8}\\)\u00a0 X 1\\(\\frac{7}{8}\\) =<br \/>\nfrist we write mixed fraction into fraction as (1 X 8 + 7 by 8) =<br \/>\n\\(\\frac{15}{8}\\) X \\(\\frac{15}{8}\\) =\\(\\frac{15 X 15}{8 X 8}\\) =<br \/>\n\\(\\frac{225}{64}\\) square feet, So 2 sky lighta are there so<br \/>\n\\(\\frac{225}{64}\\) + \\(\\frac{225}{64}\\) as<br \/>\ndenominators are same we add numerators as<br \/>\n(225 +225 = 450) we get \\(\\frac{450}{64}\\) square feet,<br \/>\nWe have area of rectangle as 140 square feet and 2 skylights as<br \/>\n\\(\\frac{450}{64}\\) square feet, So we will paint<br \/>\n140 &#8211; \\(\\frac{450}{64}\\) = \\(\\frac{8960-450}{64}\\) =<br \/>\n\\(\\frac{8510}{64}\\) as numerator is greater we write as<br \/>\n(132 X 64 + 62 by 64) = 132\\(\\frac{62}{64}\\) square feet<br \/>\ni will paint.<\/p>\n<p><strong>Performance Task<\/strong><br \/>\n<strong>Space Explorers<\/strong><br \/>\nAt the beginning of this chapter, you watched a STEAM video called \u201cSpace is Big.\u201d<br \/>\nYou are now ready to complete the performance task for this video, available at BigIdeasMath.com. Be sure to use the problem-solving complan as you work through the performance task.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27403\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-332.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 2 Fractions and Decimals 332\" width=\"289\" height=\"205\" \/><\/p>\n<h3>Fractions and Decimals Chapter Review<\/h3>\n<p><strong>2 Chapter Review<\/strong><\/p>\n<p><strong>Review Vocabulary<\/strong><\/p>\n<p><strong>Write the de\ufb01nition and give an example of each vocabulary term.<\/strong><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27404\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-333.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 2 Fractions and Decimals 333\" width=\"513\" height=\"35\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-333.png 513w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-333-300x20.png 300w\" sizes=\"(max-width: 513px) 100vw, 513px\" \/><br \/>\nReciprocals or Multiplicative Invesrses :<br \/>\nA reciprocal, or multiplicative inverse, is simply one of a pair of<br \/>\nnumbers that, when multiplied together, equal 1.<br \/>\nIf you can reduce the number to a fraction, finding the<br \/>\nreciprocal is simply a matter of transposing the numerator and<br \/>\nthe denominator.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-54514\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-98.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-98\" width=\"480\" height=\"279\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-98.bmp 480w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-98-300x174.jpg 300w\" sizes=\"(max-width: 480px) 100vw, 480px\" \/><\/p>\n<p><strong>Graphic Organizers<\/strong><\/p>\n<p>You can use a Summary Triangle to explain a concept. Here is an example of a Summary Triangle for dividing fractions.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27405\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-334.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 2 Fractions and Decimals 334\" width=\"467\" height=\"372\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-334.png 467w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-334-300x239.png 300w\" sizes=\"(max-width: 467px) 100vw, 467px\" \/><\/p>\n<p><strong>Choose and complete a graphic organizer to help you study the concept.<\/strong><\/p>\n<ol>\n<li>multiplying fractions<\/li>\n<li>multiplying mixed numbers<\/li>\n<li>reciprocals<\/li>\n<li>dividing mixed numbers<\/li>\n<li>adding and subtracting decimals<\/li>\n<li>multiplying decimals by decimals<\/li>\n<li>dividing whole numbers<\/li>\n<li>dividing decimals by decimals<\/li>\n<\/ol>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27406\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-335.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 2 Fractions and Decimals 335\" width=\"256\" height=\"362\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-335.png 256w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-335-212x300.png 212w\" sizes=\"(max-width: 256px) 100vw, 256px\" \/><\/p>\n<p>1. multiplying fractions:<\/p>\n<p>To multiply fractions :<br \/>\na. Simplify the resulting fraction if possible.<br \/>\n<span style=\"font-size: 16px;\">b. Simplify the fractions if not in lowest terms.<br \/>\n<\/span><span style=\"font-size: 16px;\">c. Multiply the numerators of the fractions to get the new numerator,<br \/>\n<\/span><span style=\"font-size: 16px;\">Multiply the denominators of the fractions to get the new denominator.<\/span><\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-54512\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-97.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-97\" width=\"649\" height=\"355\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-97.bmp 649w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-97-300x164.jpg 300w\" sizes=\"(max-width: 649px) 100vw, 649px\" \/><\/p>\n<p>2. multiplying mixed numbers :<br \/>\nA mixed number is a number that contains a whole number and a fraction,<br \/>\nfor instance 2\\(\\frac{1}{2}\\) is a mixed number.<br \/>\nMixed numbers can be multiplied by first converting them<br \/>\nto improper fractions. Below are the general rules for<br \/>\nmultiplying mixed numbers:<br \/>\n<span style=\"font-size: 16px;\">* Convert the mixed numbers to improper fractions first.<br \/>\n<\/span><span style=\"font-size: 16px;\">* Multiply the numerators from each fraction to each other<br \/>\nand place the product at the top.<br \/>\n<\/span><span style=\"font-size: 16px;\">* Multiply the denominators of each fraction by each other<br \/>\n(the numbers on the bottom). The product is the denominator<br \/>\nof the new fraction.<br \/>\n<\/span>* Simplify or reduce the final answer to the lowest terms possible.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-54522\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-99.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-99\" width=\"546\" height=\"696\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-99.bmp 546w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-99-235x300.jpg 235w\" sizes=\"(max-width: 546px) 100vw, 546px\" \/><\/p>\n<p>3. reciprocals :<\/p>\n<p>The\u00a0reciprocal\u00a0or\u00a0multiplicative inverse\u00a0of a number <span id=\"MathJax-Element-1-Frame\" class=\"MathJax\" style=\"font-style: normal; line-height: normal; font-size: 16px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px;\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mi&gt;x&lt;\/mi&gt;&lt;\/math&gt;\"><\/span><\/p>\n<p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>x<\/mi><\/math><\/p>\n<p>is the number which, when multiplied by\u00a0<span id=\"MathJax-Element-2-Frame\" class=\"MathJax\" style=\"font-style: normal; line-height: normal; font-size: 16px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px;\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mi&gt;x&lt;\/mi&gt;&lt;\/math&gt;\"><span id=\"MathJax-Span-4\" class=\"math\" role=\"math\"><span id=\"MathJax-Span-5\" class=\"mrow\"><span id=\"MathJax-Span-6\" class=\"mi\">x<\/span><\/span><\/span><\/span>\u00a0, gives\u00a0<span id=\"MathJax-Element-3-Frame\" class=\"MathJax\" style=\"font-style: normal; line-height: normal; font-size: 16px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px;\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mn&gt;1&lt;\/mn&gt;&lt;\/math&gt;\"><span id=\"MathJax-Span-7\" class=\"math\" role=\"math\"><span id=\"MathJax-Span-8\" class=\"mrow\"><span id=\"MathJax-Span-9\" class=\"mn\">1,<br \/>\n<\/span><\/span><\/span><\/span>So, the product of a number and its reciprocal is <span id=\"MathJax-Element-4-Frame\" class=\"MathJax\" style=\"font-style: normal; line-height: normal; font-size: 16px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px;\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mn&gt;1&lt;\/mn&gt;&lt;\/math&gt;\"><\/span><\/p>\n<p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mn>1<\/mn><\/math><\/p>\n<p>.<br \/>\n(This is sometimes called\u00a0the property of reciprocals),<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-54527\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-100.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-100\" width=\"532\" height=\"242\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-100.bmp 532w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-100-300x136.jpg 300w\" sizes=\"(max-width: 532px) 100vw, 532px\" \/><\/p>\n<p>4. dividing mixed numbers :<br \/>\nSteps for dividing mixed numbers.<br \/>\n<span style=\"font-size: 16px;\">a. Change each <\/span>mixed<span style=\"font-size: 16px;\"><strong>\u00a0<\/strong>number to an improper fraction.<br \/>\n<\/span><span style=\"font-size: 16px;\">b. Multiply by the reciprocal of the divisor, simplifying if possible.<br \/>\n<\/span><span style=\"font-size: 16px;\">c. Put answer in lowest terms.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-54530\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-101.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-101\" width=\"554\" height=\"698\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-101.bmp 554w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-101-238x300.jpg 238w\" sizes=\"(max-width: 554px) 100vw, 554px\" \/><br \/>\n<\/span><\/p>\n<p>5. adding and subtracting decimals :<br \/>\nStep 1: Line up the numbers vertically so that the decimal<br \/>\npoints all lie on a vertical line.<br \/>\nStep 2: Add extra zeros to the right of the number so that<br \/>\neach number has the same number of digits to the right<br \/>\nof the decimal place.<br \/>\nStep 3: Subtract the numbers as you would whole numbers.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-54534\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-102.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-102\" width=\"699\" height=\"680\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-102.bmp 699w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-102-300x292.jpg 300w\" sizes=\"(max-width: 699px) 100vw, 699px\" \/><\/p>\n<p><span style=\"font-size: 16px;\">\u00a0<\/span><\/p>\n<p><strong>Chapter Self-Assessment<\/strong><\/p>\n<p>As you complete the exercises, use the scale below to rate your understanding of the success criteria in your journal.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27407\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-336.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 2 Fractions and Decimals 336\" width=\"633\" height=\"79\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-336.png 633w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-336-300x37.png 300w\" sizes=\"(max-width: 633px) 100vw, 633px\" \/><\/p>\n<p><strong>2.1 Multiplying Fractions (pp. 45-52)<\/strong><\/p>\n<p><strong>Multiply. Write the answer in simplest form.<\/strong><\/p>\n<p>Question 1.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27408\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-337.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 2 Fractions and Decimals 337\" width=\"59\" height=\"45\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27408\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-337.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 2 Fractions and Decimals 337\" width=\"59\" height=\"45\" \/>= \\(\\frac{16}{99}\\),<br \/>\nExplanation:<br \/>\nGiven expression as \\(\\frac{2}{9}\\) X\\(\\frac{8}{11}\\) =<br \/>\nStep I: We multiply the numerators as 2 X 8 = 16<br \/>\nStep II: We multiply the denominators as 9 X 11 =99<br \/>\nStep III: We write the fraction in the simplest form as<br \/>\n\\(\\frac{16}{99}\\),<br \/>\nSo \\(\\frac{2}{9}\\) X\\(\\frac{8}{11}\\) = \\(\\frac{16}{99}\\).<\/p>\n<p>Question 2.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27409\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-338.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 2 Fractions and Decimals 338\" width=\"64\" height=\"54\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27409\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-338.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 2 Fractions and Decimals 338\" width=\"64\" height=\"54\" \/>= \\(\\frac{6}{25}\\),<br \/>\nExplanation:<br \/>\nGiven expression as \\(\\frac{3}{10}\\) X \\(\\frac{4}{5}\\) =<br \/>\nStep I: We multiply the numerators as 3 X 4 = 12<br \/>\nStep II: We multiply the denominators as 10 X 5 =50<br \/>\nStep III: We write the fraction in the simplest form as<br \/>\n\\(\\frac{12}{50}\\), as both goes in 2 we<br \/>\ncan further simplify as 2 X 6 = 12, 2 X 25 = 50, (6,25) = \\(\\frac{6}{25}\\),<br \/>\nSo \\(\\frac{3}{10}\\) X \\(\\frac{4}{5}\\) = \\(\\frac{6}{25}\\).<\/p>\n<p>Question 3.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27410\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-339.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 2 Fractions and Decimals 339\" width=\"77\" height=\"53\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27410\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-339.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 2 Fractions and Decimals 339\" width=\"77\" height=\"53\" \/>= \\(\\frac{184}{15}\\) or 12\\(\\frac{4}{15}\\),<br \/>\nExplanation:<br \/>\nGiven expression as 2\\(\\frac{3}{10}\\) X 5\\(\\frac{1}{3}\\),<br \/>\nwe write mixed fraction as fraction 2\\(\\frac{3}{10}\\) =<br \/>\n(2 x 10 + 3 by 10)\u00a0 = \\(\\frac{23}{10}\\) and 5\\(\\frac{1}{3}\\) as<br \/>\n( 5 X 3 + 1 by 3) = \\(\\frac{16}{3}\\), Now we multiply as<br \/>\n\\(\\frac{23}{10}\\) X \\(\\frac{16}{3}\\)<br \/>\nStep I: We multiply the numerators as 23 X 16 = 368<br \/>\nStep II: We multiply the denominators as 10 X 3 =30<br \/>\nStep III: We write the fraction in the simplest form as<br \/>\n\\(\\frac{368}{30}\\), as both goes in 2,<br \/>\nwe\u00a0 can further simplify as 2 X 184 = 368, 2 X 15 = 30, (184,15) = \\(\\frac{184}{15}\\),<br \/>\nas numerator is greater we write as (12 X 15 + 4 by 15) = 12\\(\\frac{4}{15}\\),<br \/>\nSo 2\\(\\frac{3}{10}\\) X 5\\(\\frac{1}{3}\\) = \\(\\frac{184}{15}\\) or 12\\(\\frac{4}{15}\\).<\/p>\n<p>Question 4.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27411\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-340.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 2 Fractions and Decimals 340\" width=\"70\" height=\"45\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27411\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-340.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 2 Fractions and Decimals 340\" width=\"70\" height=\"45\" \/>= \\(\\frac{80}{63}\\) or 1\\(\\frac{17}{63}\\),<br \/>\nExplanation:<br \/>\nGiven expression as \\(\\frac{2}{7}\\) X 4\\(\\frac{4}{9}\\),<br \/>\nwe write mixed fraction as fraction 4\\(\\frac{4}{9}\\) =<br \/>\n(4 x 9 + 4 by 9)\u00a0 = \\(\\frac{40}{9}\\), Now we multiply as<br \/>\n\\(\\frac{2}{7}\\) X \\(\\frac{40}{9}\\)<br \/>\nStep I: We multiply the numerators as 2 X 40 = 80<br \/>\nStep II: We multiply the denominators as 7 X 9 =63<br \/>\nStep III: We write the fraction in the simplest form as<br \/>\n\\(\\frac{80}{63}\\), as numerator is greater we write as<br \/>\n(1 X 63 + 17 by 63) = 1\\(\\frac{17}{63}\\),<br \/>\nSo, \\(\\frac{2}{7}\\) X 4\\(\\frac{4}{9}\\) = \\(\\frac{80}{63}\\) or 1\\(\\frac{17}{63}\\).<\/p>\n<p>Question 5.<br \/>\nWrite two fractions whose product is \\(\\frac{21}{32}\\).<\/p>\n<p>The two fractions can be \\(\\frac{7}{8}\\) or \\(\\frac{3}{4}\\),<br \/>\nwhose product is \\(\\frac{21}{32}\\),<\/p>\n<p>Explanation:<br \/>\nGiven to find two fractions whose product is \\(\\frac{21}{32}\\),<br \/>\nWe can take factors of 21 are 1, 3, 7, 21, So numerators can be<br \/>\n(1,21) or (3, 7), now factors of 32 are 1, 2, 4, 8, 16, and 32,<br \/>\ndenominators can be (1, 32) or (2, 16) or (4, 8), So the two fractions<br \/>\ncan be \\(\\frac{7}{8}\\) or \\(\\frac{3}{4}\\) whose<br \/>\nproduct is \u00a0\\(\\frac{7 X 3 }{8 X 4}\\) or \\(\\frac{21}{32}\\).<\/p>\n<p>Question 6.<br \/>\nA costume designer needs to make 12 costumes for the school play.<br \/>\nEach costume requires 2\\(\\frac{2}{3}\\) yards of fabric.<br \/>\nHow many yards of fabric does the costume designer need to<br \/>\nmake all the costumes?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27412\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-341.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 2 Fractions and Decimals 341\" width=\"194\" height=\"197\" \/><br \/>\nThe costume designer need 32 yards of fabric to<br \/>\nmake all the costumes,<\/p>\n<p>Explanation:<br \/>\nGiven a\u00a0costume designer needs to make 12 costumes<br \/>\nfor the school play. Each costume requires 2\\(\\frac{2}{3}\\) yards of fabric.<br \/>\nSo for 12 costumes we require 12 X 2\\(\\frac{2}{3}\\) yards of fabric=<br \/>\nfirst we write mixed fraction into fraction as 2\\(\\frac{2}{3}\\) =<br \/>\n(2 X 3 + 2 by 3) = \\(\\frac{8}{3}\\) So 12 X \\(\\frac{8}{3}\\) =<br \/>\n\\(\\frac{12 X 8}{3}\\) = \\(\\frac{96}{3}\\)\u00a0 as it goes in 3,<br \/>\n3 X 32 = 96 we get \\(\\frac{96}{3}\\) = 32.<br \/>\ntherefore the costume designer need 32 yards of fabric to<br \/>\nmake all the costumes.<\/p>\n<p>Question 7.<br \/>\nYou spend \\(\\frac{4}{5}\\) of an hour on your homework.<br \/>\nYou spend \\(\\frac{1}{2}\\) of that time working on your<br \/>\nscience homework. How many minutes do you spend working on<br \/>\nscience homework?<\/p>\n<p>I have spent 24 minutes working on science homework,<\/p>\n<p>Explanation:<br \/>\nGiven I spend \\(\\frac{4}{5}\\) of an hour on my homework.<br \/>\nI have\u00a0 spend \\(\\frac{1}{2}\\) of that time working on my<br \/>\nscience homework. So time spent for working on science homework is<br \/>\n\\(\\frac{4}{5}\\) X \\(\\frac{1}{2}\\) = \\(\\frac{4 X 1}{5 X 2}\\) =<br \/>\n\\(\\frac{4}{10}\\) as further can be simplified as both<br \/>\ngoes in 2, 2 X 2 = 4 ,\u00a0 2 X 5 = 10, (2, 5) = \\(\\frac{2}{5}\\) hours,<br \/>\nnow we convert into minutes as 1 hour is equal to<br \/>\n60 minutes, So \\(\\frac{2}{5}\\) X 60 = \\(\\frac{2 X 60}{5}\\)\u00a0 =<br \/>\n\\(\\frac{120}{5}\\)\u00a0 as 5 X 24 =120 we get \\(\\frac{120}{5}\\) = 24,<br \/>\ntherefore I have spent 24 minutes working on science homework.<\/p>\n<p><strong>2.2 Dividing Fractions (pp. 53-60)<\/strong><\/p>\n<p>Divide. Write the answer in simplest form.<\/p>\n<p>Question 8.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27413\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-342.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 2 Fractions and Decimals 342\" width=\"62\" height=\"44\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27413\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-342.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 2 Fractions and Decimals 342\" width=\"62\" height=\"44\" \/> = \\(\\frac{9}{10}\\),<br \/>\nExplanation:<br \/>\nGiven expressions as \\(\\frac{3}{4}\\) \u00f7 \\(\\frac{5}{6}\\),<br \/>\nwe write reciprocal of the fraction \\(\\frac{5}{6}\\) as \\(\\frac{6}{5}\\)<br \/>\nand multiply as \\(\\frac{3}{4}\\) X \\(\\frac{6}{5}\\) =<br \/>\n\\(\\frac{3 X 6}{4 X 5}\\) = \\(\\frac{18}{20}\\),<br \/>\nwe can further simplify as both goes in 2, 2 X 9 = 18 and 2 X 10 = 20,<br \/>\n(9,10)=\\(\\frac{9}{10}\\). Therefore \\(\\frac{3}{4}\\) \u00f7<br \/>\n\\(\\frac{5}{6}\\) = \\(\\frac{9}{10}\\).<\/p>\n<p>Question 9.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27414\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-343.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 2 Fractions and Decimals 343\" width=\"54\" height=\"46\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27414\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-343.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 2 Fractions and Decimals 343\" width=\"54\" height=\"46\" \/>= \\(\\frac{1}{20}\\),<br \/>\nExplanation:<br \/>\nGiven expressions as \\(\\frac{2}{5}\\) \u00f7 8<br \/>\nwe write reciprocal of the fraction 8 as \\(\\frac{1}{8}\\)<br \/>\nand multiply as \\(\\frac{2}{5}\\) X \\(\\frac{1}{8}\\) =<br \/>\n\\(\\frac{2 X 1}{5 X 8}\\) = \\(\\frac{2}{40}\\),<br \/>\nwe can further simplify as both goes in 2, 2 X 1 = 2 and 2 X 20 = 40,<br \/>\n(1,20)=\\(\\frac{1}{20}\\). Therefore \\(\\frac{2}{5}\\) \u00f7 8<br \/>\n= \\(\\frac{1}{20}\\).<\/p>\n<p>Question 10.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27415\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-344.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 2 Fractions and Decimals 344\" width=\"58\" height=\"47\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27415\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-344.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 2 Fractions and Decimals 344\" width=\"58\" height=\"47\" \/>= 15<br \/>\nExplanation:<br \/>\nGiven expressions as 5 \u00f7 \\(\\frac{1}{3}\\),<br \/>\nwe write reciprocal of the fraction \\(\\frac{1}{3}\\) as 3<br \/>\nand multiply as 5 X 3 =15, Therefore 5 \u00f7 \\(\\frac{1}{3}\\) = 15.<\/p>\n<p>Question 11.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27416\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-345.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 2 Fractions and Decimals 345\" width=\"60\" height=\"51\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27416\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-345.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 2 Fractions and Decimals 345\" width=\"60\" height=\"51\" \/>= \\(\\frac{80}{27}\\) = 2\\(\\frac{26}{27}\\),<br \/>\nExplanation:<br \/>\nGiven expressions as \\(\\frac{8}{9}\\) \u00f7 \\(\\frac{3}{10}\\),<br \/>\nwe write reciprocal of the fraction \\(\\frac{8}{9}\\) as \\(\\frac{10}{3}\\)<br \/>\nand multiply as \\(\\frac{8}{9}\\) X \\(\\frac{10}{3}\\) =<br \/>\n\\(\\frac{8 X 10}{9 X 3}\\) = \\(\\frac{80}{27}\\),<br \/>\nas numerator is greater we write as ( 2 X 27 + 26 by 27)= 2\\(\\frac{26}{27}\\).<br \/>\nTherefore \\(\\frac{8}{9}\\) \u00f7 \\(\\frac{3}{10}\\) = \\(\\frac{80}{27}\\) = 2\\(\\frac{26}{27}\\).<\/p>\n<p>Question 12.<br \/>\nA box contains 10 cups of pancake mix. You use \\(\\frac{2}{3}\\) cup<br \/>\neach time you make pancakes. How many times can you make pancakes?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27417\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-346.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 2 Fractions and Decimals 346\" width=\"178\" height=\"144\" \/><br \/>\nWe can make 15 times pancakes,<\/p>\n<p>Explanation:<br \/>\nGiven a box contains 10 cups of pancake mix. I use \\(\\frac{2}{3}\\) cup<br \/>\neach time you make pancakes, So number of times I<br \/>\ncan make pancakes are 10 \u00f7 \\(\\frac{2}{3}\\) =<br \/>\nwe write reciprocal of the fraction \\(\\frac{2}{3}\\) as \\(\\frac{3}{2}\\)<br \/>\nand multiply as 10 X \\(\\frac{3}{2}\\) = \\(\\frac{10 X 3}{2}\\) =<br \/>\n\\(\\frac{30}{2}\\) as 30 goes in 2 we get \\(\\frac{30}{2}\\) = 15,<br \/>\ntherefore we can make 15 times pancakes.<\/p>\n<p>Question 13.<br \/>\nWrite two fractions whose quotient is \\(\\frac{28}{45}\\).<\/p>\n<p>Explanation:<\/p>\n<p>The two fractions can be \\(\\frac{4}{9}\\) \u00f7 \u00a0\\(\\frac{5}{7}\\) whose<br \/>\nquotient is \\(\\frac{28}{45}\\).<\/p>\n<p>Explanation:<br \/>\nGiven to find two fractions whose quotient is \\(\\frac{28}{45}\\),<br \/>\nWe can take factors of 28 are \u00a01, 2, 4, 7, 14 and 28, So numerators can be<br \/>\n(1,28) or (2, 14) or (4, 7), now factors of 45 are 1, 3, 5, 9, 15, and 45,<br \/>\ndenominators can be (1, 45) or (3, 15) or (5, 9) and 45<br \/>\nfactors will be reciprocal, So the two fractions can be<br \/>\n\\(\\frac{4}{9}\\) \u00f7 \\(\\frac{5}{7}\\) now we calculate<br \/>\nas \\(\\frac{4}{9}\\) X \\(\\frac{7}{5}\\)<br \/>\nquotient is \\(\\frac{4 X 7}{9 X 5}\\) = \\(\\frac{28}{45}\\).<\/p>\n<p><strong>2.3 Dividing Mixed Numbers (pp. 61\u201366)<\/strong><\/p>\n<p><strong>Divide. Write the answer in simplest form.<\/strong><\/p>\n<p>Question 14.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27418\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-347.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 2 Fractions and Decimals 347\" width=\"61\" height=\"45\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27418\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-347.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 2 Fractions and Decimals 347\" width=\"61\" height=\"45\" \/>= 2\\(\\frac{9}{20}\\),<br \/>\nExplanation:<br \/>\nGiven expressions as 1\\(\\frac{2}{5}\\) \u00f7 \\(\\frac{4}{7}\\),<br \/>\nwe write mixed fraction as ( 1 X 5 + 2 by 5) = \\(\\frac{7}{5}\\),<br \/>\nwe write reciprocal of the fraction \\(\\frac{4}{7}\\) as \\(\\frac{7}{4}\\)<br \/>\nand multiply as \\(\\frac{7}{5}\\) X \\(\\frac{7}{4}\\) =<br \/>\n\\(\\frac{7 X 7}{5 X 4}\\) = \\(\\frac{49}{20}\\),<br \/>\nas numerator is greater we write as ( 2 X 20 + 9 by 20)= 2\\(\\frac{9}{20}\\).<br \/>\nTherefore 1\\(\\frac{2}{5}\\) \u00f7 \\(\\frac{4}{7}\\) = \\(\\frac{49}{20}\\) = 2\\(\\frac{9}{20}\\).<\/p>\n<p>Question 15.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27419\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-348.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 2 Fractions and Decimals 348\" width=\"69\" height=\"56\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27419\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-348.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 2 Fractions and Decimals 348\" width=\"69\" height=\"56\" \/>= 1\\(\\frac{7}{8}\\),<br \/>\nExplanation:<br \/>\nGiven expressions as 5\\(\\frac{5}{8}\\) \u00f7 3,<br \/>\nwe write mixed fraction as ( 5 X 8 + 5 by 8) = \\(\\frac{45}{8}\\),<br \/>\nwe write reciprocal of 3 as \\(\\frac{1}{3}\\)<br \/>\nand multiply as \\(\\frac{45}{8}\\) X \\(\\frac{1}{3}\\) =<br \/>\n\\(\\frac{45 X 1}{8 X 3}\\) = \\(\\frac{45}{24}\\), as both<br \/>\ngoes in 3, we get 3 X 15 = 45, 3 X 8 = 24,(15,8) = \\(\\frac{15}{8}\\)<br \/>\nas numerator is greater we write as ( 1 X 8 + 7 by 8)= 1\\(\\frac{7}{8}\\),<br \/>\nTherefore 5\\(\\frac{5}{8}\\) \u00f7 3 = 1\\(\\frac{7}{8}\\).<\/p>\n<p>Question 16.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27420\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-349.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 2 Fractions and Decimals 349\" width=\"64\" height=\"54\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27420\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-349.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 2 Fractions and Decimals 349\" width=\"64\" height=\"54\" \/> = 1\\(\\frac{3}{4}\\),<br \/>\nExplanation:<br \/>\nGiven expressions as 5 \u00f7 2\\(\\frac{6}{7}\\) ,<br \/>\nwe write mixed fraction as ( 2 X 7 + 6 by 7) = \\(\\frac{20}{7}\\),<br \/>\nwe write reciprocal of \\(\\frac{20}{7}\\) as \\(\\frac{7}{20}\\)<br \/>\nand multiply as 5 X \\(\\frac{7}{20}\\) =<br \/>\n\\(\\frac{5 X 7}{1 X 20}\\) = \\(\\frac{35}{20}\\), as both<br \/>\ngoes in 5, we get 5 X 7 = 35, 5 X 4 = 20,(7,4) = \\(\\frac{7}{4}\\)<br \/>\nas numerator is greater we write as ( 1 X 4 + 3 by 4)= 1\\(\\frac{3}{4}\\),<br \/>\nTherefore 5 \u00f7 2\\(\\frac{6}{7}\\) = 1\\(\\frac{3}{4}\\).<\/p>\n<p>Question 17.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27421\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-350.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 2 Fractions and Decimals 350\" width=\"77\" height=\"52\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27421\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-350.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 2 Fractions and Decimals 350\" width=\"77\" height=\"52\" \/>= 1\\(\\frac{5}{6}\\),<br \/>\nExplanation:<br \/>\nGiven expressions as 4\\(\\frac{1}{8}\\) \u00f7 2\\(\\frac{1}{4}\\),<br \/>\nwe write mixed fraction 4\\(\\frac{1}{8}\\) as (4 X 8 + 1 by 8) =<br \/>\n\\(\\frac{33}{8}\\) and 2\\(\\frac{1}{4}\\) as (2 X 4 + 1 by 4) =<br \/>\n\\(\\frac{9}{4}\\) now we write reciprocal of the fraction<br \/>\n\\(\\frac{9}{4}\\) as \\(\\frac{4}{9}\\)<br \/>\nand multiply as \\(\\frac{33}{8}\\) X \\(\\frac{4}{9}\\) =<br \/>\n\\(\\frac{33 X 4}{8 X 9}\\) = \\(\\frac{132}{72}\\),<br \/>\nas both goes in 12, 12 X 11 = 132, 12 X 6 = 72, (11,6) = \\(\\frac{11}{6}\\)<br \/>\nas numerator is greater we write as ( 1 X 6 + 5 by 6)= 1\\(\\frac{5}{6}\\).<br \/>\nTherefore 4\\(\\frac{1}{8}\\) \u00f7 2\\(\\frac{1}{4}\\) = 1\\(\\frac{5}{6}\\).<\/p>\n<p>Question 18.<br \/>\nEvaluate <img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27423\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-351.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 2 Fractions and Decimals 351\" width=\"90\" height=\"43\" \/>. Write the answer in simplest form.<br \/>\n5\\(\\frac{5}{7}\\) \u00f7 1\\(\\frac{3}{5}\\)X 4\\(\\frac{2}{3}\\) =<br \/>\n16\\(\\frac{2}{3}\\),<\/p>\n<p>Explanation:<br \/>\nGiven expressions as 5\\(\\frac{5}{7}\\) \u00f7 1\\(\\frac{3}{5}\\) X<br \/>\n4\\(\\frac{2}{3}\\), first we write mixed fraction 5\\(\\frac{5}{7}\\) as<br \/>\n(5 X 7 + 5 by 7) = \\(\\frac{40}{7}\\) and 1\\(\\frac{3}{5}\\)<br \/>\nas (1 X 5 + 3 by 5) = \\(\\frac{8}{5}\\) now we write reciprocal of the fraction<br \/>\n\\(\\frac{8}{5}\\) as \\(\\frac{5}{8}\\)<br \/>\nand multiply as \\(\\frac{40}{7}\\) X \\(\\frac{5}{8}\\) =<br \/>\n\\(\\frac{40 X 5}{7 X 8}\\) = \\(\\frac{200}{56}\\),<br \/>\nas both goes in 8, 8 X 25 = 200, 8 X 7 = 56, (25,7) = \\(\\frac{25}{7}\\),<br \/>\nNow we write 4\\(\\frac{2}{3}\\)\u00a0 as ( 4 X 3 + 2 by 3) = \\(\\frac{14}{3}\\),<br \/>\nwe multiply as \\(\\frac{25}{7}\\) X \\(\\frac{14}{3}\\) =<br \/>\n\\(\\frac{25 X 14}{7 X 3}\\) = \\(\\frac{350}{21}\\), as both goes<br \/>\nin 7 as 7 X 50 = 350, 7 X 3 = 21, (50, 3) = \\(\\frac{50}{3}\\),<br \/>\nas numerator is greater we write as ( 16 X 3 + 2 by 3)= 16\\(\\frac{2}{3}\\),<br \/>\nTherefore 5\\(\\frac{5}{7}\\) \u00f7 1\\(\\frac{3}{5}\\) X<br \/>\n4\\(\\frac{2}{3}\\) = 16\\(\\frac{2}{3}\\).<\/p>\n<p>Question 19.<br \/>\nYou have 23\\(\\frac{1}{2}\\) pounds of blueberries to store in freezer bags.<br \/>\nEach bag holds 3\\(\\frac{3}{4}\\) pounds of blueberries.<br \/>\nWhat is the minimum number of freezer bags needed to store all the blueberries?<\/p>\n<p>7 freezer bags minimum are needed to store all the blueberries.<\/p>\n<p>Explanation:<br \/>\nGiven I\u00a0have 23\\(\\frac{1}{2}\\) pounds of blueberries to<br \/>\nstore in freezer bags. Each bag holds 3\\(\\frac{3}{4}\\) pounds<br \/>\nof blueberries. Minimum number of freezer bags needed to<br \/>\nstore all the blueberries 23\\(\\frac{1}{2}\\) \u00f7 3\\(\\frac{3}{4}\\) =<br \/>\nWe write 23\\(\\frac{1}{2}\\) as\u00a0 (23 X 2 + 1 by 2) = \\(\\frac{47}{2}\\),<br \/>\nand 3\\(\\frac{3}{4}\\) as ( 3 X 4 + 3 by 4) = \\(\\frac{15}{4}\\),<br \/>\nnow we write \\(\\frac{15}{4}\\) as reciprocal \\(\\frac{4}{15}\\)<br \/>\nand multiply as \\(\\frac{47}{2}\\) X \\(\\frac{4}{15}\\)\u00a0 =<br \/>\n\\(\\frac{47 X 4}{2 X 15}\\)\u00a0 = \\(\\frac{188}{30}\\) as both<br \/>\ngoes in 2, 2 X 94 = 188, 2 X 15 = 30, (94, 15) = \\(\\frac{94}{15}\\) ,<br \/>\nas numerator is greater we write as (6 X 15 + 4 by 15) = 6\\(\\frac{4}{15}\\),<br \/>\nSo approximately we require 7 freezer bags minimum<br \/>\nneeded to store all the blueberries.<\/p>\n<p>Question 20.<br \/>\nA squirrel feeder holds 4\\(\\frac{1}{2}\\) cups of seeds.<br \/>\nAnother squirrel feeder holds 6\\(\\frac{7}{8}\\) cups of seeds.<br \/>\nOne scoop of seeds is 1\\(\\frac{5}{8}\\) cups.<br \/>\nHow many scoops of seeds do you need to \ufb01ll both squirrel feeders?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27422\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-2-Fractions-and-Decimals-351.1.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 2 Fractions and Decimals 351.1\" width=\"152\" height=\"213\" \/><\/p>\n<p>7 scoops of seeds we need to fill both squirrel feeders,<\/p>\n<p>Explanation:<br \/>\nGiven a\u00a0squirrel feeder holds 4\\(\\frac{1}{2}\\) cups of seeds.<br \/>\nAnother squirrel feeder holds 6\\(\\frac{7}{8}\\) cups of seeds.<br \/>\nOne scoop of seeds is 1\\(\\frac{5}{8}\\) cups.<br \/>\nSo first squirrel feeder needs 4\\(\\frac{1}{2}\\) \u00f7 1\\(\\frac{5}{8}\\),<br \/>\nWe write 4\\(\\frac{1}{2}\\) as (4 X 2 + 1 by 2) = \\(\\frac{9}{2}\\)<br \/>\nand 1\\(\\frac{5}{8}\\) = (1X 8 + 5 by 8) = \\(\\frac{13}{8}\\),<br \/>\nnow we write \\(\\frac{13}{8}\\) reciprocal and multiply as<br \/>\n\\(\\frac{9}{2}\\) X \\(\\frac{8}{13}\\) = \\(\\frac{9 x 8}{2 X 13}\\) =<br \/>\n\\(\\frac{72}{26}\\) as both goes in 2, 2 X 36 = 72, 2 X 13 = 26, (36,13) =<br \/>\n\\(\\frac{36}{13}\\),<br \/>\nNow second squirrel feeder needs 6\\(\\frac{7}{8}\\) \u00f7 1\\(\\frac{5}{8}\\),<br \/>\nWe write 6\\(\\frac{7}{8}\\) as (6 X 8 + 7 by 8) = \\(\\frac{55}{8}\\),<br \/>\nnow we have 1\\(\\frac{5}{8}\\) = (1X 8 + 5 by 8) = \\(\\frac{13}{8}\\),<br \/>\nnow we write \\(\\frac{13}{8}\\) reciprocal and multiply as<br \/>\n\\(\\frac{55}{8}\\) X \\(\\frac{8}{13}\\) = \\(\\frac{55 X 8}{8 X 13}\\) =<br \/>\n\\(\\frac{440}{104}\\) as both goes in 8, 8 X 55 = 440, 8 X 13 = 104,<br \/>\n(55, 13) = \\(\\frac{55}{13}\\), Now we have feeder 1 and feeder 2,<br \/>\nso total is \\(\\frac{36}{13}\\) + \\(\\frac{55}{13}\\) as<br \/>\nboth have same denomiators we add numerators and write as<br \/>\n\\(\\frac{36 + 55}{13}\\) = \\(\\frac{91}{13}\\) as 91 goes<br \/>\nin 13( 13 X 7 = 91) we get \\(\\frac{91}{13}\\) = 7,therefore<br \/>\n7 scoops of seeds we need to fill both squirrel feeders.<\/p>\n<p><strong>2.4 Adding and Subtracting Decimals (pp. 67\u201372)<\/strong><\/p>\n<p><strong>Add.<\/strong><\/p>\n<p>Question 21.<br \/>\n3.78 + 8.94<br \/>\n3.78 + 8.94 = 12.72,<\/p>\n<p>Explanation:<br \/>\nGiven expression 3.78 + 8.94 we add as<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a01,1\u00a0\u00a0<\/span><br \/>\n3.78<br \/>\n<span style=\"text-decoration: underline;\">+8.94<br \/>\n12.72<br \/>\n<\/span>Therefore, 3.78 + 8.94 = 12.72.<\/p>\n<p>Question 22.<br \/>\n19.89 + 4.372<br \/>\n19.89 + 4.372 = 24.262,<\/p>\n<p>Explanation:<br \/>\nGiven expression 19.89 + 4.372 we add as<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 1,1,1\u00a0\u00a0<\/span><br \/>\n19.890<br \/>\n<span style=\"text-decoration: underline;\">+ 4.372<br \/>\n24.262<br \/>\n<\/span>Therefore, 19.89 + 4.372 = 24.262.<\/p>\n<p>Question 23.<br \/>\n24.916 + 17.385<br \/>\n24.916 + 17.385 = 42.301,<\/p>\n<p>Explanation:<br \/>\nGiven expression 24.916 + 17.385\u00a0 we add as<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 1,1,1,1\u00a0\u00a0<\/span><br \/>\n24.916<br \/>\n<span style=\"text-decoration: underline;\">+ 17.385<br \/>\n42.301<br \/>\n<\/span>Therefore, 24.916 + 17.385 = 42.301.<\/p>\n<p><strong>Subtract.<\/strong><\/p>\n<p>Question 24.<br \/>\n7.638 &#8211; 2.365<br \/>\n7.638 &#8211; 2.365 = 5.273,<\/p>\n<p>Explanation:<br \/>\nGiven expression 7.638 &#8211; 2.365\u00a0 we subtract as<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 5,13\u00a0\u00a0<\/span><br \/>\n7.638<br \/>\n<span style=\"text-decoration: underline;\">&#8211; 2.365<br \/>\n5.273<br \/>\n<\/span>Therefore, 7.638 &#8211; 2.365 = 5.273.<\/p>\n<p>Question 25.<br \/>\n14.21 &#8211; 4.103<br \/>\n14.21 &#8211; 4.103 = 10.107,<\/p>\n<p>Explanation:<br \/>\nGiven expression 14.21 &#8211; 4.103 we subtract as<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a014,13,10\u00a0\u00a0<\/span><br \/>\n14.210<br \/>\n<span style=\"text-decoration: underline;\">&#8211;\u00a0 4.103<br \/>\n10.107<br \/>\n<\/span>Therefore, 14.21 &#8211; 4.103 = 10.107.<\/p>\n<p>Question 26.<br \/>\n5.467 &#8211; 2.736<br \/>\n5.467 &#8211; 2.736 = 2.731,<\/p>\n<p>Explanation:<br \/>\nGiven expression 5.467 &#8211; 2.736 we subtract as<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 4,14\u00a0\u00a0<\/span><br \/>\n5.467<br \/>\n<span style=\"text-decoration: underline;\">&#8211; 2.736<br \/>\n2.731<br \/>\n<\/span>Therefore, 5.467 &#8211; 2.736 = 2.731.<\/p>\n<p>Question 27.<br \/>\nWrite three decimals that have a sum of 10.806.<\/p>\n<p>The three decimals are 4.203, 3.769, 2.834\u00a0 which<br \/>\nwill have a sum of 10.806,<\/p>\n<p>Explanation:<br \/>\nTo make sum of 10.806 we can take decimals as<br \/>\n4.203, 3.769, 2.834\u00a0 and check as<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 1,1,1\u00a0\u00a0<\/span><br \/>\n4.203<br \/>\n3.769<br \/>\n<span style=\"text-decoration: underline;\">+2.834<br \/>\n10.806<br \/>\n<\/span>therefore the three decimals are 4.203, 3.769, 2.834<br \/>\nwhich will have a sum of 10.806.<\/p>\n<p>Question 28.<br \/>\nTo make fuel for the main engines of a space shuttle,<br \/>\n102,619.377 kilograms of liquid hydrogen and 616,496.4409 kilograms<br \/>\nof liquid oxygen are mixed together in the external tank.<br \/>\nHow much fuel is stored in the external tank?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27163\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-352.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 352\" width=\"240\" height=\"285\" \/><\/p>\n<p>Fuel stored in the external tank is 719,115.786 kilograms,<\/p>\n<p>Explanation:<br \/>\nGiven to make fuel for the main engines of a space shuttle,<br \/>\n102,619.377 kilograms of liquid hydrogen and 616,496.4409 kilograms<br \/>\nof liquid oxygen are mixed together in the external tank.<br \/>\nSo fuel is stored in the external tank is<br \/>\n102,619.377 + 616,496.4409 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 1,1,1,\u00a0 1\u00a0 \u00a0 \u00a0\u00a0<\/span><br \/>\n102,619.3770<br \/>\n<span style=\"text-decoration: underline;\">+616,496.4409<br \/>\n719115.8179<br \/>\n<\/span>Therefore, fuel stored in the external tank is 719,115.786 kilograms.<\/p>\n<p><strong>2.5 Multiplying Decimals (pp. 73\u201380)<\/strong><\/p>\n<p><strong>Multiply. Use estimation to check your answer.<\/strong><\/p>\n<p>Question 29.<br \/>\n26.174 \u00d7 79<br \/>\n26.174 X 79 = 2067.746,<\/p>\n<p>Explanation:<br \/>\nGiven expression 26.174 X 79 we add as<br \/>\n<span style=\"text-decoration: underline;\">4,1,5,2<\/span><br \/>\n<span style=\"text-decoration: underline;\">5,1,6,3\u00a0\u00a0<\/span><br \/>\n26.174 &#8212;&#8212; 3 decimal places<br \/>\n<span style=\"text-decoration: underline;\">X\u00a0 \u00a079<br \/>\n<\/span>\u00a0 235566<br \/>\n<span style=\"text-decoration: underline;\">1832180<br \/>\n2067.746&#8212;&#8212; 3 decimal places<br \/>\n<\/span>Therefore, 26.174 X 79 = 2067.746.<\/p>\n<p>Question 30.<br \/>\n9.475 \u00d7 8.03<br \/>\n9.475 \u00d7 8.03 = 76.08425,<\/p>\n<p>Explanation:<br \/>\nGiven expression 9.475 X 8.03 we add as<br \/>\n3,6,4<br \/>\n<span style=\"text-decoration: underline;\">1,2,1\u00a0\u00a0<\/span><br \/>\n9.475 &#8212;&#8212; 3 decimal places<br \/>\n<span style=\"text-decoration: underline;\">X 8.03 &#8212;&#8211; 2 decimal places<br \/>\n<\/span>0028425<br \/>\n0000000<span style=\"text-decoration: underline;\"><br \/>\n7580000<br \/>\n76.08425&#8212;&#8212;5 decimal places<br \/>\n<\/span>Therefore, 9.475 \u00d7 8.03 = 76.08425.<\/p>\n<p>Question 31.<br \/>\n0.051 \u00d7 0.244<br \/>\n0.051 \u00d7 0.244 = 0.012444,<\/p>\n<p>Explanation:<br \/>\nGiven expression 9.475 X 8.03 we add as<br \/>\n<u>\u00a01\u00a0 \u00a0 \u00a0 \u00a0\u00a0<\/u><br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a02\u00a0 \u00a0 \u00a0 <\/span><br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a02\u00a0 \u00a0 \u00a0<\/span><br \/>\n0.051 &#8212;&#8212; 3 decimal places<br \/>\n<span style=\"text-decoration: underline;\">X 0.244 &#8212;&#8211; 3 decimal places<\/span><br \/>\n0000204<br \/>\n0002040<span style=\"text-decoration: underline;\"><br \/>\n<\/span>0110200<span style=\"text-decoration: underline;\"><br \/>\n0000000<br \/>\n0.012444&#8212;&#8212;6 decimal places<br \/>\n<\/span>Therefore, 0.051 \u00d7 0.244 = 0.012444.<\/p>\n<p>Question 32.<br \/>\nEvaluate 3.76(2.43 + 9.8).<br \/>\n3.76(2.43 + 9.8) = 45.9848,<\/p>\n<p>Explanation:<br \/>\nGiven expression as 3.76(2.43 + 9.8),<br \/>\nFirst we calculate (2.43 + 9.8) =<br \/>\n2.43<br \/>\n<span style=\"text-decoration: underline;\">+9.8<br \/>\n12.23<br \/>\n<\/span>Now 3.76 X 12.23 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a01,1,2\u00a0\u00a0<\/span><br \/>\n<span style=\"text-decoration: underline;\">\u00a0 1,1,1<br \/>\n<\/span>12.23 &#8212;&#8212; 2 decimal places<span style=\"text-decoration: underline;\"><br \/>\nX3.76 &#8212;&#8212; 2 decimal places<br \/>\n<\/span>0073.38<br \/>\n085610<span style=\"text-decoration: underline;\"><br \/>\n36.6900<br \/>\n45.9848 &#8212;-4 decimal places<br \/>\n<\/span>therfeore, 3.76(2.43 + 9.8) = 45.9848.<\/p>\n<p>Question 33.<br \/>\nHair grows about 1.27 centimeters each month.<br \/>\nHow much does hair grow in 4 months?<\/p>\n<p>5.08 centimeters hair will grow in 4 months,<\/p>\n<p>Explanation:<br \/>\nGiven hair grows about 1.27 centimeters each month.<br \/>\nso hair growth in 4 months is 4 X 1.27 =<br \/>\n<span style=\"text-decoration: underline;\">1,2\u00a0\u00a0<\/span><br \/>\n1.27<br \/>\n<span style=\"text-decoration: underline;\">X 4<br \/>\n5.08<br \/>\n<\/span>Therefore, 5.08 centimeters hair will grow in 4 months.<\/p>\n<p><strong>2.6 Dividing Whole Numbers (pp. 81\u201386)<\/strong><\/p>\n<p><strong>Divide. Use estimation to check your answer.<\/strong><\/p>\n<p>Question 34.<br \/>\n7296 \u00f7 38<br \/>\n7296 \u00f7 38 = 192,<br \/>\nEstimation is reasonable,<\/p>\n<p>Explanation:<br \/>\nGiven 7296 \u00f7 38 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 192<\/span><br \/>\n38)7296\u00a0 \u00a0 38 X 1 = 38<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a038<br \/>\n<\/span>\u00a0 \u00a0 \u00a0349\u00a0 \u00a0 \u00a038 X 9 = 342<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0342<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a076\u00a0 \u00a038 X 2 = 76<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a076<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 0<br \/>\nTherefore 7296 \u00f7 38 = 192,<br \/>\nEstimation is 7300 \u00f7 38 = 192.1,<br \/>\nSo estimation is reasonable.<\/p>\n<p>Question 35.<br \/>\n5081 \u00f7 203<br \/>\n5081 \u00f7 203 = 25.02,<br \/>\nEstimation is reasonable,<\/p>\n<p>Explanation:<br \/>\nGiven 5081 \u00f7 203 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 25.02\u00a0<\/span><br \/>\n203)5081\u00a0 \u00a0 \u00a0203 X 2 = 406<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0406<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a01021\u00a0 \u00a0 203 X 5 = 1015<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a01015<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 6\u00a0 \u00a0 \u00a0203 X 0.02 = 4.06<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 4.06<br \/>\n1.94\u00a0 reaminder<br \/>\n<\/span>Therefore 5081 \u00f7 203 = 25.02,<br \/>\nEstimation is 5100 \u00f7 203 = 25.123<br \/>\nSo estimation is reasonable.<\/p>\n<p>Question 36.<br \/>\n\\(\\frac{17,264}{128}\\)<br \/>\n\\(\\frac{17,264}{128}\\) = 134.875,<br \/>\nEstimation is approximately reasonable,<\/p>\n<p>Explanation:<br \/>\nGiven 17264 \u00f7 128 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 134.875\u00a0<\/span><br \/>\n128)17264\u00a0 \u00a0 128 X 1 = 128<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0128<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0446\u00a0 \u00a0 \u00a0128 X 3 = 384<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0384<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 624\u00a0 128 X 4 = 512<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 512<br \/>\n<\/span>\u00a0 \u00a0112\u00a0 \u00a0128 X 0.8 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0102.4<\/span><br \/>\n9.6\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0128 X 0.07 = 8.96<span style=\"text-decoration: underline;\"><br \/>\n8.96<br \/>\n<\/span>0.64\u00a0 128 X 0.005 = 0.64<span style=\"text-decoration: underline;\"><br \/>\n0.64<br \/>\n<\/span>\u00a00<span style=\"text-decoration: underline;\"><br \/>\n<\/span>Therefore \\(\\frac{17,264}{128}\\) = 134.875<br \/>\nEstimation is 17,000 \u00f7 128 = 132.8125<br \/>\nSo estimation is approximately reasonable.<\/p>\n<p>Question 37.<br \/>\nYour local varsity basketball team offers bus transportation for a<br \/>\nplayoff game. Each bus holds 56 people. A total of 328 people sign up.<br \/>\nAll buses are full except for the last bus. How many buses are used?<br \/>\nHow many people are in the last bus?<\/p>\n<p>6 buses are used and in the last bus<br \/>\nthere are 48 people.<\/p>\n<p>Explanation:<br \/>\nGiven my local varsity basketball team offers bus transportation for a<br \/>\nplayoff game. Each bus holds 56 people. A total of 328 people sign up.<br \/>\nSo, buses used are 328 \u00f7 56 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a05<\/span><br \/>\n56)328\u00a0 \u00a0 56 X 5 = 280<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0280<\/span><br \/>\n48 remainder<br \/>\nwe got 5 buses + 48 people,<br \/>\nTherefore we need total 6 buses and in the last bus<br \/>\nthere are 48 people.<\/p>\n<p>Question 38.<br \/>\nYou have 600 elastic bands to make railroad bracelets.<br \/>\nHow many complete bracelets can you make?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27164\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-353.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 353\" width=\"213\" height=\"188\" \/><\/p>\n<p>15 bracelets I can make,<\/p>\n<p>Explanation:<br \/>\nGiven 600 elastic bands to make railroad bracelets<br \/>\nand we need for one bracelet 28 elastic bands for<br \/>\nouter rails and 10 elastic bands for inner track,<br \/>\nmeans 28 + 10 = 38 elastic bands for one bracelet,<br \/>\nFrom 600 we can make 600 \u00f7 38 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a015.78<\/span><br \/>\n38)600\u00a0 \u00a0 \u00a038 X 1 = 38<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a038<br \/>\n<\/span>\u00a0 \u00a0 \u00a0220\u00a0 \u00a0 \u00a038 X 5 = 190<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0190<\/span><br \/>\n30\u00a0 \u00a0 \u00a038 X 0.7 = 26.6<br \/>\n<span style=\"text-decoration: underline;\">26.6<br \/>\n<\/span>3.4\u00a0 \u00a038 X 0.08 = 3.04<br \/>\n<span style=\"text-decoration: underline;\">\u00a03.04<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a00.36 remainder<br \/>\ntherefore, it means I can make 15 railroad bracelets<br \/>\nfrom 600 elastic bands.<\/p>\n<p><strong>2.7 Dividing Decimals (pp. 87\u201394)<\/strong><\/p>\n<p><strong>Divide. Check your answer.<\/strong><\/p>\n<p>Question 39.<br \/>\n0.498 \u00f7 6<br \/>\n0.498 \u00f7 6 = 0.083,<\/p>\n<p>Explanation:<br \/>\nGiven 0.498\u00f7 6 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 0.083<\/span><br \/>\n6)0.498\u00a0 \u00a0 \u00a0 6 X 0.08 = 0.48<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a00.48<br \/>\n<\/span>\u00a0 \u00a0 0.018\u00a0 \u00a0 \u00a06 X 0.003 = 0.018<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 0.018<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a00<br \/>\nTherefore 0.498 \u00f7 6 = 0.083.<\/p>\n<p>Question 40.<br \/>\n8.9 \u00f7 0.356<br \/>\n8.9 \u00f7 0.356 = 25<\/p>\n<p>Explanation:<br \/>\nGiven 8.9\u00f7 0.356 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a025\u00a0 \u00a0 \u00a0<\/span><br \/>\n0.356)8.9\u00a0 \u00a0 \u00a0 0.356 X\u00a0 25 = 8.9<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 8.9<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 0<br \/>\nTherefore 8.9 \u00f7 0.356 = 8.9.<\/p>\n<p>Question 41.<br \/>\n21.85 \u00f7 3.8<br \/>\n21.85 \u00f7 3.8 = 5.75<\/p>\n<p>Explanation:<br \/>\nGiven 21.85 \u00f7 3.8 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a05.75\u00a0 \u00a0 \u00a0<\/span><br \/>\n3.8)21.85\u00a0 \u00a0 \u00a0 3.8 X 5 = 19<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 19<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 2.85\u00a0 \u00a0 \u00a0 \u00a03.8 X 0.7 = 2.66<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 2.66<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a00.19\u00a0 \u00a0 \u00a0 \u00a0 3.8 X 0.05 = 0.19<br \/>\n0.19<br \/>\nTherefore 21.85 \u00f7 3.8 = 5.75.<\/p>\n<p>Question 42.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27162\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-254.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 254\" width=\"173\" height=\"48\" \/><br \/>\n(14.075 + 24.67) \u00f7\u00a0 3.15 = 12.3,<\/p>\n<p>Explanation:<br \/>\nGiven expression as (14.075 + 24.67) \u00f7\u00a0 3.15,<br \/>\nfirst we calculate (14.075 + 24.67) = 38.745 now<br \/>\n38.745 \u00f7\u00a0 3.15 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 12.3\u00a0<\/span><br \/>\n3.15)38.745\u00a0 \u00a0 3.15 X 12 = 37.8<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 37.8<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 0.945\u00a0 \u00a0 3.15 X 0.3 = 0.945<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 0.945<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a00<br \/>\nTherefore, (14.075 + 24.67) \u00f7\u00a0 3.15 = 12.3.<\/p>\n<p>Question 43.<br \/>\nYour beginning balance on your lunch account is $42.<br \/>\nYou buy lunch for $1.80 every day and sometimes buy a snack for $0.85.<br \/>\nAfter 20 days, you have a balance of $0.05. How many snacks did you buy?<\/p>\n<p>I buyed 7 snacks in 20 days,<\/p>\n<p>Explanation:<br \/>\nGiven my beginning balance on lunch account is $42.<br \/>\nI buy lunch for $1.80 every day and sometimes buy a snack<br \/>\nfor $0.85. After 20 days, I have a balance of $0.05.<br \/>\nSo for 20 days I buyed for lunch is 20 X $1.80 =<br \/>\n$36 and have balance left of $0.05 means 36 + 0.05 = $36.05,<br \/>\nNow I spent on snacks is $42 &#8211; $36.05 = $5.95 and snack<br \/>\ncosts $0.85, So number of snacks I did buyed is<br \/>\n$5.95 \u00f7\u00a0 $0.85 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a07\u00a0 \u00a0<\/span><br \/>\n0.85)5.95\u00a0 \u00a00.85 X 7 = 5.95<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 5.95<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 0<br \/>\ntherefore, I buyed 7 snacks in 20 days.<\/p>\n<h3>Fractions and Decimals Practice Test<\/h3>\n<p><strong>2 Practice Test<\/strong><\/p>\n<p><strong>Evaluate the expression. Write the answer in simplest form.<\/strong><\/p>\n<p>Question 1.<br \/>\n5.138 + 2.624<br \/>\n5.138 + 2.624 = 7.762<\/p>\n<p>Explanation:<br \/>\nGiven expression 24.916 + 17.385\u00a0 we add as<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 1\u00a0 \u00a0<\/span><br \/>\n5.138<span style=\"text-decoration: underline;\"><br \/>\n+2.624<br \/>\n7.762<br \/>\n<\/span>Therefore, 5.138 + 2.624 = 7.762.<\/p>\n<p>Question 2.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27165\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-354.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 354\" width=\"63\" height=\"47\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27165\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-354.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 354\" width=\"63\" height=\"47\" \/>= \\(\\frac{7}{4}\\) or 1\\(\\frac{3}{4}\\),<\/p>\n<p>Explanation:<br \/>\nGiven expressions as \\(\\frac{5}{6}\\) \u00f7 \\(\\frac{10}{21}\\),<br \/>\nwe write reciprocal of the fraction \\(\\frac{10}{21}\\) as \\(\\frac{21}{10}\\)<br \/>\nand multiply as \\(\\frac{5}{6}\\) X \\(\\frac{21}{10}\\) =<br \/>\n\\(\\frac{5 X 21}{6 X 10}\\) = \\(\\frac{105}{60}\\),<br \/>\nwe can further simplify as both goes in 15, 15 X 7 = 105 and 15 X 4 = 60,<br \/>\n(7, 4)= \\(\\frac{7}{4}\\) as numerator is greater we write as<br \/>\n(1 X 4 + 3 by 4) = 1\\(\\frac{3}{4}\\), Therefore \\(\\frac{5}{6}\\) \u00f7<br \/>\n\\(\\frac{10}{21}\\) = \\(\\frac{7}{4}\\) = 1\\(\\frac{3}{4}\\).<\/p>\n<p>Question 3.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27166\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-355.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 355\" width=\"82\" height=\"38\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27166\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-355.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 355\" width=\"82\" height=\"38\" \/> = 21.84,<br \/>\nExplanation:<br \/>\nGiven 5.46 \u00f7 0.25 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 21.84\u00a0 \u00a0 \u00a0<\/span><br \/>\n0.25)5.46\u00a0 \u00a0 \u00a0 0.25 X 21 = 5.25<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 5.25<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 0.21\u00a0 \u00a0 \u00a0 0.25 X 0.8 = 0.2<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 0.20<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a00.01\u00a0 \u00a0 \u00a0 \u00a00.25 X 0.04 = 0.01<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a00.01<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a00<br \/>\nTherefore 5.46 \u00f7 0.25 = 21.84.<\/p>\n<p>Question 4.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27167\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-356.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 356\" width=\"62\" height=\"50\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27167\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-356.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 356\" width=\"62\" height=\"50\" \/>= \\(\\frac{3}{8}\\),<br \/>\nExplanation:<br \/>\nGiven expression as \\(\\frac{9}{16}\\) X \\(\\frac{2}{3}\\) =<br \/>\nStep I: We multiply the numerators as 9 X 2 = 18<br \/>\nStep II: We multiply the denominators as 16 X 3 =48<br \/>\nStep III: We write the fraction in the simplest form as<br \/>\n\\(\\frac{18}{48}\\), as both goes in 6 we<br \/>\ncan further simplify as 6 X 3 = 18, 6 X 8 = 48, (3, 8) = \\(\\frac{3}{8}\\),<br \/>\nSo \\(\\frac{9}{16}\\) X \\(\\frac{2}{3}\\) = \\(\\frac{3}{8}\\).<\/p>\n<p>Question 5.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27168\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-357.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 357\" width=\"77\" height=\"49\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27168\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-357.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 357\" width=\"77\" height=\"49\" \/>= \\(\\frac{70}{23}\\) = 3\\(\\frac{1}{23}\\),<br \/>\nExplanation:<br \/>\nGiven expressions as 8\\(\\frac{3}{4}\\) \u00f7 2\\(\\frac{7}{8}\\),<br \/>\nwe write mixed fraction 8\\(\\frac{3}{4}\\) as (8 X 4 + 3 by 4) =<br \/>\n\\(\\frac{35}{4}\\) and 2\\(\\frac{7}{8}\\) as (2 X 8 + 7 by 8) =<br \/>\n\\(\\frac{23}{8}\\) now we write reciprocal of the fraction<br \/>\n\\(\\frac{23}{8}\\) as \\(\\frac{8}{23}\\)<br \/>\nand multiply as \\(\\frac{35}{4}\\) X \\(\\frac{8}{23}\\) =<br \/>\n\\(\\frac{35 X 8}{4 X 23}\\) = \\(\\frac{280}{92}\\),<br \/>\nas both goes in 4, 4 X 70 = 280, 4 X 23 = 92, (70, 23) = \\(\\frac{70}{23}\\)<br \/>\nas numerator is greater we write as (3 X 23 + 1 by 23)= 3\\(\\frac{1}{23}\\).<br \/>\nTherefore 8\\(\\frac{3}{4}\\) \u00f7 2\\(\\frac{7}{8}\\) = \\(\\frac{70}{23}\\) = 3\\(\\frac{1}{23}\\),<\/p>\n<p>Question 6.<br \/>\n4.87 \u00d7 7.23<br \/>\n4.87 \u00d7 7.23 = 35.2101,<\/p>\n<p>Explanation:<br \/>\nGiven expression 4.87 X 7.23 we add as<br \/>\n<span style=\"text-decoration: underline;\">6,4<\/span><br \/>\n<span style=\"text-decoration: underline;\">1,1<\/span><br \/>\n<span style=\"text-decoration: underline;\">2,2,2\u00a0\u00a0<\/span><br \/>\n4.87 &#8212;&#8212; 2 decimal places<br \/>\n<span style=\"text-decoration: underline;\">X7.23&#8212;-\u00a0 2 decimal places<br \/>\n<\/span>001461<br \/>\n009740<span style=\"text-decoration: underline;\"><br \/>\n340900<br \/>\n35.2101&#8212;&#8212;4 decimal places<br \/>\n<\/span>Therefore, 4.87 \u00d7 7.23 = 35.2101,<\/p>\n<p>Question 7.<br \/>\n1875 \u00f7 125<br \/>\n1875 \u00f7 125 = 15,<\/p>\n<p>Explanation:<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 15\u00a0 \u00a0<\/span><br \/>\n125)1875\u00a0 \u00a0 125 X 1 = 125<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0125<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0625\u00a0 \u00a0 125 X 5 = 625<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0625<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 0<br \/>\nTherefore, 1875 \u00f7 125 = 15.<\/p>\n<p>Question 8.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27169\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-358.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 358\" width=\"64\" height=\"44\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27169\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-358.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 358\" width=\"64\" height=\"44\" \/>= 25,<br \/>\nExplanation:<br \/>\nGiven expressions as 10 \u00f7 \\(\\frac{2}{5}\\),<br \/>\nnow we write reciprocal of the fraction<br \/>\n\\(\\frac{2}{5}\\) as \\(\\frac{5}{2}\\)<br \/>\nand multiply as 10 X \\(\\frac{5}{2}\\) =<br \/>\n\\(\\frac{10 X 5}{1 X 2}\\) = \\(\\frac{50}{2}\\),<br \/>\nas both goes in 2, 2 X 25 = 50, 2 X 1 = 2, (25, 1) = \\(\\frac{50}{2}\\) = 25,<br \/>\nTherefore 10 \u00f7 \\(\\frac{2}{5}\\) = 25.<\/p>\n<p>Question 9.<br \/>\n57.82 \u00f7 0.784<br \/>\n57.82 \u00f7 0.784 = 73.75,<\/p>\n<p>Explanation:<br \/>\nGiven expression as 57.82 \u00f7 0.784 =<br \/>\n<span style=\"text-decoration: underline;\">73.75<\/span><br \/>\n0.784)57.82\u00a0 \u00a00.784 X 7 = 57.232<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a057.232<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 0.588\u00a0 \u00a00.784 X 0.7 = 0.5488<span style=\"text-decoration: underline;\"><br \/>\n0.5488<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 0.0392\u00a0 0.784 X 0.05 = 0.0392<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 0.0392<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 0<span style=\"text-decoration: underline;\"><br \/>\n<\/span>Therefore, 57.82 \u00f7 0.784 = 73.75.<\/p>\n<p>Question 10.<br \/>\n5.316 \u00f7 1.942<br \/>\n5.316 \u00f7 1.942 = 2.737,<\/p>\n<p>Explanation:<br \/>\nGiven expression as 5.316 \u00f7 1.942 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a02.737<\/span><br \/>\n1.942)5.316\u00a0 \u00a0 1.942 X 2 = 3.884<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 3.884<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 1.432\u00a0 \u00a0 1.942 X 0.7 = 1.3594<span style=\"text-decoration: underline;\"><br \/>\n1.3594<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 0.0726\u00a0 \u00a01.942 X 0.03 = 0.05826<span style=\"text-decoration: underline;\"><br \/>\n0.05826<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a00.01434\u00a0 1.942 X 0.007 = 0.013594<span style=\"text-decoration: underline;\"><br \/>\n0.013594<br \/>\n0.000746 remainder<br \/>\n<\/span>therefore 5.316 \u00f7 1.942 = 2.737.<\/p>\n<p>Question 11.<br \/>\n6.729 \u00d7 8.3<br \/>\n6.729 \u00d7 8.3 = 55.8507,<\/p>\n<p>Explanation:<br \/>\nGiven expression as 6.729 X 8.3 =<br \/>\n5,2,7<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 2,2<\/span><br \/>\n6.729&#8212;&#8212; 3 decimal places<br \/>\n<span style=\"text-decoration: underline;\">X 8.3 &#8212;&#8212; 1 decimal place<br \/>\n<\/span>020187<br \/>\n<span style=\"text-decoration: underline;\">538320<br \/>\n55.8507&#8212;&#8212; 4 decimal places<\/span><\/p>\n<p>Question 12.<br \/>\n\\(\\frac{13,376}{248}\\)<br \/>\n\\(\\frac{13,376}{248}\\) = 53.935,<\/p>\n<p>Explanation:<br \/>\nGiven expression as \\(\\frac{13,376}{248}\\),<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a053.935<\/span><br \/>\n248)13376\u00a0 \u00a0 248 X 5 = 1240<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a01240\u00a0<\/span><br \/>\n976\u00a0 \u00a0 248 X 3 = 744<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0744<\/span><br \/>\n232\u00a0 \u00a0 248 X 0.9 = 223.2<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0223.2<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a08.8\u00a0 \u00a0248 X 0.03 = 7.44<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a07.44<\/span><br \/>\n1.36\u00a0 248 X 0.005 = 1.24<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a01.24<\/span><br \/>\n0.12 remainder<br \/>\ntherefore \\(\\frac{13,376}{248}\\) = 53.935.<\/p>\n<p>Question 13.<br \/>\nOn a road trip, you notice that the gas tank is \\(\\frac{1}{4}\\) full.<br \/>\nThe gas tank can hold 18 gallons, and the vehicle averages 22 miles per gallon.<br \/>\nWill you make it to your destination 110 miles away before you run out of gas?<br \/>\nExplain.<\/p>\n<p>No, I cannot make it to destination, I will be running out of gas,<\/p>\n<p>Explanation:<br \/>\nGiven on a road trip, you notice that the gas tank is \\(\\frac{1}{4}\\) full.<br \/>\nThe gas tank can hold 18 gallons, and the vehicle averages<br \/>\n22 miles per gallon. Will I make it to my destination 110 miles<br \/>\naway before I run out of gas, First we calculate tank has<br \/>\n18 X \\(\\frac{1}{4}\\) = \\(\\frac{18}{4}\\) , as both<br \/>\ngoes in 2 we get 2 X 9 = 18, 2 X 2 = 4, (9, 2) = \\(\\frac{9}{2}\\) gallon,<br \/>\nnow we have the vehicle averages 22 miles per gallon means<br \/>\n22 X \\(\\frac{9}{2}\\) = \\(\\frac{198}{2}\\) as<br \/>\nit goes in 2 we get 2 X 99 = 198, 2 X 1 = 2, \\(\\frac{198}{2}\\) =99,<br \/>\nas 99 is less than 110 miles no, I cannot make it to destination,<br \/>\nI will be running out of gas.<\/p>\n<p>Question 14.<br \/>\nFor a diving event, the highest and the lowest of seven scores<br \/>\nare discarded. Next, the total of the remaining scores is multiplied<br \/>\nby the degree of difficulty of the dive. That value is then multiplied<br \/>\nby 0.6 to determine the \ufb01nal score. Find the \ufb01nal score for the dive.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27170\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-359.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 359\" width=\"561\" height=\"99\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-359.png 561w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-359-300x53.png 300w\" sizes=\"(max-width: 561px) 100vw, 561px\" \/><\/p>\n<p>The final score for the dive is 73.47,<\/p>\n<p>Explanation:<br \/>\nGiven for a diving event, the highest and the lowest of seven scores<br \/>\nare discarded. Next, the total of the remaining scores is multiplied<br \/>\nby the degree of difficulty of the dive. That value is then multiplied<br \/>\nby 0.6 to determine the \ufb01nal score.<br \/>\nAfter discarding the highest and the lowest of seven scores-<br \/>\n9.0, 7.0 we have remaining scores as 8, 7.5, 8, 8.5, 7.5,<br \/>\nnow we add as 8 +7.5 + 8 +8.5 + 7.5 = 39.5, So the total of the<br \/>\nremaining scores is multiplied by the degree of difficulty<br \/>\nof the dive, given the difficulty of the dive as 3.1,<br \/>\nSo 39.5 X 3.1 =<br \/>\n<span style=\"text-decoration: underline;\">2,1<\/span><br \/>\n39.5 &#8212;&#8212; 1 decimal place<br \/>\n<span style=\"text-decoration: underline;\">X3.1<\/span> &#8212;&#8212; 1 decimal place<br \/>\n00395<br \/>\n<span style=\"text-decoration: underline;\">11850<\/span><br \/>\n<span style=\"text-decoration: underline;\">122.45&#8212;&#8212; 2 decimal places<br \/>\n<\/span>Now 122.45 is multiplied by 0.6 to determine the \ufb01nal score as<br \/>\n122.45 X 0.6 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a01,1,2,3<\/span><br \/>\n122.45<span style=\"text-decoration: underline;\">&#8212;&#8212; 2 decimal places<\/span><br \/>\n<span style=\"text-decoration: underline;\">X 0.6\u00a0 &#8212;&#8212; 1 decimal place<br \/>\n<\/span>073470<br \/>\n<span style=\"text-decoration: underline;\">000000<br \/>\n73.470&#8212;&#8212; 3 decimal places,<br \/>\n<\/span>So, The final score for the dive is 73.47.<\/p>\n<p>Question 15.<br \/>\nYou are cutting as many 20\\(\\frac{1}{2}\\)-inch pieces<br \/>\nfrom the board to make ladder steps for a tree fort.<br \/>\nHow many steps can you make? How much wood is left over?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27171\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-360.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 360\" width=\"254\" height=\"88\" \/><br \/>\nI can make 5 steps and \\(\\frac{35}{41}\\)-inch piece<br \/>\nwood will be left over.<\/p>\n<p>Explanation:<br \/>\nGiven I am cutting as many 20\\(\\frac{1}{2}\\)-inch pieces<br \/>\nfrom the board of 120 in to make ladder steps for a tree fort.<br \/>\nNumber of steps I can make are 120 \u00f7 20\\(\\frac{1}{2}\\),<br \/>\nfirst we write mixed fraction into fraction and write<br \/>\nreciprocal then multiply as 20\\(\\frac{1}{2}\\) = ( 20 X 2 + 1 by 2) =<br \/>\n\\(\\frac{41}{2}\\), now reciprocal as \\(\\frac{2}{41}\\)<br \/>\nand multiply as 120 X \\(\\frac{2}{41}\\) = \\(\\frac{240}{41}\\),<br \/>\nas numerator is greater we write as (5 X 41 + 35 by 41) = 5\\(\\frac{35}{41}\\),<br \/>\nSo, I can make 5 steps and \\(\\frac{35}{41}\\)-inch piece<br \/>\nwood will be left over.<\/p>\n<p>Question 16.<br \/>\nYou spend 2\\(\\frac{1}{2}\\)-hours online.<br \/>\nYou spend \\(\\frac{1}{5}\\) of that time writing a blog.<br \/>\nHow long do you spend writing your blog?<\/p>\n<p>I have spent 12\\(\\frac{1}{2}\\) hours for writng blog,<\/p>\n<p>Explanation:<br \/>\nGiven I spend 2\\(\\frac{1}{2}\\)-hours online and<br \/>\nspent \\(\\frac{1}{5}\\) of that time writing a blog.<br \/>\nSo I spend writing my blog for 2\\(\\frac{1}{2}\\) \u00f7 \\(\\frac{1}{5}\\) =<br \/>\nfirst we write mixed fraction as fraction 2\\(\\frac{1}{2}\\) =<br \/>\n(2 X 2 + 1 by 2) = \\(\\frac{5}{2}\\) \u00f7 \\(\\frac{1}{5}\\) now<br \/>\nwe write \u00a0\\(\\frac{1}{5}\\) as reciprocal we get 5 and multiply,<br \/>\n\\(\\frac{5}{2}\\) X 5 = \\(\\frac{5 X 5 }{2}\\) = \\(\\frac{25}{2}\\),<br \/>\nas numerator is greater we write as ( 2 X 12 + 1 by 2) = 12\\(\\frac{1}{2}\\),<br \/>\nTherefore I have spent 12\\(\\frac{1}{2}\\) hours for writng blog.<\/p>\n<p>Question 17.<br \/>\nYou and a friend take pictures at a motocross event.<br \/>\nYour camera can take 24 pictures in 3.75 seconds.<br \/>\nYour friend\u2019s camera can take 36 pictures in 4.5 seconds.<br \/>\nEvaluate the expression (36 \u00f7 4.5) (24 \u00f7 3.75) to \ufb01nd how many<br \/>\ntimes faster your friend\u2019s camera is than your camera.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27172\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-361.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 361\" width=\"213\" height=\"253\" \/><\/p>\n<p>51.2 seconds times faster my friend\u2019s camera is<br \/>\nthan my camera,<\/p>\n<p>Explanation:<br \/>\nGiven expression as (36 \u00f7 4.5) (24 \u00f7 3.75) =<br \/>\nFirst we will find (36 \u00f7 4.5) =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 8\u00a0<\/span><br \/>\n4.5)36\u00a0 \u00a0 4.5 X 8 = 36<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 36<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 0<br \/>\nSo, (36 \u00f7 4.5) = 8,<br \/>\nNow we will find (24 \u00f7 3.75)=<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a06.4<\/span><br \/>\n3.75)24\u00a0 \u00a0 \u00a0 \u00a0 \u00a03.75 X 6 = 22.5<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a022.5<\/span><br \/>\n1.5\u00a0 \u00a0 \u00a0 \u00a0 3.75 X 0.4 = 1.5<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a01.5<br \/>\n<\/span>\u00a0 \u00a0 \u00a0 \u00a0 0<br \/>\nSo, (24 \u00f7 3.75) = 6.4,<br \/>\nNow 8 X 6.4 =<br \/>\n<span style=\"text-decoration: underline;\">3,<\/span><br \/>\n6.4 &#8212;&#8211; 1 decimal place<br \/>\n<span style=\"text-decoration: underline;\">X 8<br \/>\n51.2 &#8212;&#8211; 1 decimal place<br \/>\n<\/span>Therefore, 51.2 seconds times faster my friend\u2019s camera is<br \/>\nthan my camera.<\/p>\n<h3>Fractions and Decimals Cumulative Practice<\/h3>\n<p><strong>2 Cumulative Practice<\/strong><\/p>\n<p>Question 1.<br \/>\nWhich number is equivalent to the expression below?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27173\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-362.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 362\" width=\"342\" height=\"109\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-362.png 342w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-362-300x96.png 300w\" sizes=\"(max-width: 342px) 100vw, 342px\" \/><\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27174\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-363.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 363\" width=\"333\" height=\"395\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-363.png 333w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-363-253x300.png 253w\" sizes=\"(max-width: 333px) 100vw, 333px\" \/><br \/>\n6 X 8 &#8211; 2 X 3<sup>2 <\/sup>= 30, matches with B,<\/p>\n<p>Explanation:<br \/>\nGiven expression as (6 X 8 &#8211; 2 X 3<sup>2 <\/sup>) =<br \/>\nFirst we will find (2 X 3<sup>2 <\/sup>) = 2 X 3 X 3 = 18,<br \/>\nNow 6 X 8 = 48, So 48 -18 = 30,<br \/>\nTherefore (6 X 8 &#8211; 2 X 3<sup>2 <\/sup>) = 30 which matches with B.<\/p>\n<p>Question 2.<br \/>\nWhat is the greatest common factor of 48 and 120?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27175\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-364.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 364\" width=\"77\" height=\"66\" \/><br \/>\nGreatest common factor of 48 and 120 is 24,<\/p>\n<p>Explanation:<br \/>\nGiven to find greatest common factor of 48 and 120,<br \/>\nWe have factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16,\u00a0<mark>24 and<br \/>\nfactors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60,<br \/>\nHere we have the biggest common factor number is 120,<br \/>\ntherefore greatest common factor of 48 and 120 is 24.<\/mark><\/p>\n<p>Question 3.<br \/>\nWhich number is equivalent to 5.139 &#8211; 2.64?<br \/>\nF. 2.499<br \/>\nG. 2.599<br \/>\nH. 3.519<br \/>\nI. 3.599<br \/>\n5.139 &#8211; 2.64 = 2.499 equivalent to F,<\/p>\n<p>Explanation:<br \/>\nGiven to evaluate 5.139 &#8211; 2.64 =<br \/>\n5.139<br \/>\n<span style=\"text-decoration: underline;\">-2.640<br \/>\n2.499<br \/>\n<\/span>Therefore, 5.139 &#8211; 2.64 = 2.499 which equivalent to F.<\/p>\n<p>Question 4.<br \/>\nWhich number is equivalent to <img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27176\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-365.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 365\" width=\"47\" height=\"43\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27177\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-366.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 366\" width=\"333\" height=\"100\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-366.png 333w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-366-300x90.png 300w\" sizes=\"(max-width: 333px) 100vw, 333px\" \/><br \/>\n\\(\\frac{4}{9}\\) \u00f7 \\(\\frac{5}{7}\\) = \\(\\frac{28}{45}\\),<br \/>\nmatches with B.<br \/>\nExplanation:<br \/>\nGiven expressions as \\(\\frac{4}{9}\\) \u00f7 \\(\\frac{5}{7}\\),<br \/>\nwe write reciprocal of the fraction \\(\\frac{5}{7}\\) as \\(\\frac{7}{5}\\)<br \/>\nand multiply as \\(\\frac{4}{9}\\) X \\(\\frac{7}{5}\\) =<br \/>\n\\(\\frac{4 X 7}{9 X 5}\\) = \\(\\frac{28}{45}\\),<br \/>\nTherefore \\(\\frac{4}{9}\\) \u00f7 \\(\\frac{5}{7}\\) = \\(\\frac{28}{45}\\),<br \/>\nwhich matches with B.<\/p>\n<p>Question 5.<br \/>\nYou buy orange and black streamers for a party. The orange<br \/>\nstreamers are 9 feet long, and the black streamers are 12 feet long.<br \/>\nWhat are the least numbers of streamers you should buy in order for<br \/>\nthe total length of the orange streamers to be the same as the total<br \/>\nlength of the black streamers?<br \/>\nF. 36 orange streamers and 36 black streamers<br \/>\nG. 12 orange streamers and 9 black streamers<br \/>\nH. 3 orange streamers and 4 black streamers<br \/>\nI. 4 orange streamers and 3 black streamers<\/p>\n<p>The total length of the orange streamers to be the same<br \/>\nas the total length of the black streamers is<br \/>\n4 orange streamers and 3 black streamers matches with I.<\/p>\n<p>Explanation:<br \/>\nGiven I buy orange and black streamers for a party. The orange<br \/>\nstreamers are 9 feet long, and the black streamers are 12 feet long.<br \/>\nWhat are the least numbers of streamers I should buy in order for<br \/>\nthe total length of the orange streamers to be the same as the total<br \/>\nlength of the black streamers are \u00a0we first list the multiples of<br \/>\n9 and 12 and then we find the smallest multiple they have in common.<br \/>\nMultiples of 9: 9, 18, 27, 36, 45, 54, etc.<br \/>\nMultiples of 12: 12, 24, 36, 48, 60, 72, etc.<br \/>\nThe least multiple on the two lists that they have in common<br \/>\nis the LCM of 9 and 12. Therefore, the LCM of 9 and 12 is 36.<br \/>\nSo orange streamers are 36 \u00f7 9 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a04<\/span><br \/>\n9)36\u00a0 \u00a0 \u00a09 X 4 =36<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a036<br \/>\n<\/span>\u00a0 \u00a0 0<br \/>\n36 \u00f7 9 = 4,<br \/>\nand black streamers are 36 \u00f7 12 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a03<\/span><br \/>\n12)36\u00a0 \u00a0 12 X 3 = 36<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a036<\/span><br \/>\n0<br \/>\n36 \u00f7 12 = 3,<br \/>\nTherefore, The total length (36) of the orange streamers<br \/>\nto be the same as the total length of the black streamers is<br \/>\n4 orange streamers and 3 black streamers matches with I.<\/p>\n<p>Question 6.<br \/>\nWhich number is a prime factor of 572?<br \/>\nA. 4<br \/>\nB. 7<br \/>\nC. 13<br \/>\nD. 22<br \/>\n13 number is prime factor of 572 ,matches with C,<\/p>\n<p>Explanation:<br \/>\nGiven to find the number which is prime factor of 572,<br \/>\nWe have prime factors os 572 as 2, 2, 11, 13,<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-54485\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-95.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-95\" width=\"240\" height=\"327\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-95.bmp 240w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-95-220x300.jpg 220w\" sizes=\"(max-width: 240px) 100vw, 240px\" \/><br \/>\nSo from given numbers C.13 &#8211; matches.<\/p>\n<p>Question 7.<br \/>\nWhich number is equivalent to 7059 \u00f7 301?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27178\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-367.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 367\" width=\"362\" height=\"88\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-367.png 362w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-367-300x73.png 300w\" sizes=\"(max-width: 362px) 100vw, 362px\" \/><\/p>\n<p>\\(\\frac{7059}{301}\\) = 23\\(\\frac{136}{301}\\) which matches with H.<\/p>\n<p>Explanation:<br \/>\nGiven expressions as \\(\\frac{7059}{301}\\) =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 23\u00a0\u00a0<\/span><br \/>\n301)7059\u00a0 \u00a0 301 X 2 = 602<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0602<\/span><br \/>\n1039\u00a0 \u00a0301 X 3 = 903<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0903<br \/>\n136 remainder<br \/>\n<\/span>So, \\(\\frac{7059}{301}\\) = 23\\(\\frac{136}{301}\\) which matches with H.<\/p>\n<p>Question 8.<br \/>\nA square wall tile has side lengths of 4 inches. You use 360 of the tiles.<br \/>\nWhat is the area of the wall covered by the tiles?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27179\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-368.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 368\" width=\"374\" height=\"70\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-368.png 374w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-368-300x56.png 300w\" sizes=\"(max-width: 374px) 100vw, 374px\" \/><br \/>\nThe area of the wall covered by the tiles is 3760 in.<sup>2<\/sup><br \/>\nmatches with D.<\/p>\n<p>Explanation:<br \/>\nGiven a square wall tile has side lengths of 4 inches, we<br \/>\nuse 360 of the tiles, so the area of the wall covered by the tiles is<br \/>\n(we have area of sqaure is (Side X Side)) = 360 X 4 X 4 = 5760,<br \/>\nTherefore the area of the wall covered by the tiles is 3760 in.<sup>2<\/sup><br \/>\nwhich matches with D.<\/p>\n<p>Question 9.<br \/>\nWhich expression is equivalent to a perfect square?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27180\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-369.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 369\" width=\"410\" height=\"68\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-369.png 410w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-369-300x50.png 300w\" sizes=\"(max-width: 410px) 100vw, 410px\" \/><\/p>\n<p>Expression I. 3<sup>2 <\/sup>+ 6 X 5 \u00f7 3 is equivalent to a perfect square,<\/p>\n<p>Explanation:<br \/>\nGiven to find an expressions equivalent to a perfect square is<br \/>\nthe square of a number is that number times itself.<br \/>\nThe perfect squares are the squares of the whole numbers:<br \/>\n1, 4, 9, 16, 25, 36, 49, 64, 81, 100,<br \/>\nNow square roots are<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-54496\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-2-Fractions-and-Decimals-96.bmp\" alt=\"Big Ideas Math Book 6th Grade Answer Key Chapter 2 Fractions and Decimals-96\" width=\"240\" height=\"224\" \/><br \/>\nFirst we the expressions as 3 + 2<sup>2 <\/sup>X 7 = 3 + ((2 X 2) X 7) =<br \/>\n3 + ( 4 X 7) = 3 + 28 = 31, as 31 lies between 25 and 36, 5<sup>2 <\/sup>and 6<sup>2<br \/>\n<\/sup>not a perfect square,<br \/>\nNext expression is 34 + (18 \u00f7 2<sup>2 <\/sup>) =<br \/>\n34 + (18 \u00f7 (2 X 2)) = 34 + 18 \u00f7 4 = 34 + 4.5 =39.5,<br \/>\nIt lies between 36 and 49, 6<sup>2 <\/sup>and 7<sup>2<br \/>\n<\/sup>not a perfect square,<br \/>\nNext expression is (80 + 4) \u00f7 4 = 84 \u00f7 4 = 21,<br \/>\nIt lies between 16 and 25, 4<sup>2 <\/sup>and 5<sup>2<br \/>\n<\/sup>not a perfect square,<br \/>\nNext expression is 3<sup>2 <\/sup>+ 6 X 5 \u00f7 3 = (((3 X 3) + 6) X 5) \u00f7 3 =<br \/>\n((9 + 6) X 5 \u00f7 3) = (15 X 5) \u00f7 3 = 75 \u00f7 3 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a025<\/span><br \/>\n3)75\u00a0 \u00a0 3 X 2 = 6<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a06\u00a0\u00a0<\/span><br \/>\n15\u00a0 \u00a03 X 5 = 15<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a0 15<\/span><br \/>\n0<br \/>\nSo, 75 \u00f7 3 = 25, 25 is perfect square 5<sup>2 <\/sup>,<br \/>\ntherefore expression I. 3<sup>2 <\/sup>+ 6 X 5 \u00f7 3 is equivalent to a perfect square.<\/p>\n<p>Question 10.<br \/>\nWhat is the missing denominator in the expression below?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27181\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-370.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 370\" width=\"120\" height=\"65\" \/><br \/>\nA. 1<br \/>\nB. 2<br \/>\nC. 3<br \/>\nD. 8<br \/>\n3 is the missing denominator in the expression,<br \/>\nmatches with C,<\/p>\n<p>Explanation :<br \/>\nlet us take the missing denominator as x,<br \/>\ngiven expression as \\(\\frac{4}{8}\\) \u00f7 \\(\\frac{2}{x}\\) = \\(\\frac{3}{4}\\) ,<br \/>\nNow we have \\(\\frac{2}{x}\\) we write reciprocal \\(\\frac{x}{2}\\)<br \/>\nand multiply as \\(\\frac{4}{8}\\) X \\(\\frac{x}{2}\\) =<br \/>\n\\(\\frac{4 X x}{8 X 2}\\) = \\(\\frac{4x}{16}\\) both goes in 4,<br \/>\n4 X x = 4x, 4 X 4 = 16, (x, 4) = \\(\\frac{x}{4}\\) now we equate with<br \/>\n\\(\\frac{3}{4}\\) we get x = 3, Therefore 3 is the missing denominator in<br \/>\nthe expression which matches with C.<\/p>\n<p>Question 11.<br \/>\nWhat is 4.56 \u00d7 0.7?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27182\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-371.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 371\" width=\"87\" height=\"73\" \/><\/p>\n<p>Explanation:<br \/>\nGiven expression as 4.56 X 0.7 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a03,4<\/span><br \/>\n4.56\u00a0 &#8212;- 2 decimal places<br \/>\n<span style=\"text-decoration: underline;\">X 0.7&#8212;- -1\u00a0 decimal place<br \/>\n3.192 &#8212; 3 decimal places<\/span><\/p>\n<p>Therfore, 4.56 X 0.7 = 3.192.<\/p>\n<p>Question 12.<br \/>\nThe area of the large rectangle is how many times the area of the small rectangle?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27184\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-372.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 372\" width=\"271\" height=\"116\" \/><br \/>\nF. 4.4515<br \/>\nG. 5.915<br \/>\nH. 17.2575<br \/>\nI. 111.2875<br \/>\nThe area of the large rectangle is 17.2575 cm<sup>2<\/sup><br \/>\ntimes the area of the small rectangle matches with H.<\/p>\n<p>Explanation:<br \/>\nGiven large rectangle width 7.25 cm and length as 3.07 cm,<br \/>\nSo area of large rectangle is 7.25 X 3.07 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a01<\/span><br \/>\n<span style=\"text-decoration: underline;\">1,3<\/span><br \/>\n7.25 &#8212;- 2 decimal places<br \/>\n<span style=\"text-decoration: underline;\">X3.07&#8212;- 2 decimal places<\/span><br \/>\n005075<br \/>\n000000<br \/>\n<span style=\"text-decoration: underline;\">217500<br \/>\n22.2575 &#8212;- 4 decimal places<\/span><\/p>\n<p>therefore area of lare rectangle is 22.2575 cm<sup>2<\/sup>,<br \/>\nGiven small rectangle width 4 cm and length as 1.25 cm,<br \/>\nSo area of small rectangle is 4 X 1.25 =<br \/>\n<span style=\"text-decoration: underline;\">\u00a0 \u00a02<\/span><br \/>\n1.25<span style=\"text-decoration: underline;\"><br \/>\nX 4<br \/>\n5<br \/>\n<\/span>therefore area of small rectangle is 5 cm<sup>2<\/sup>,<span style=\"text-decoration: underline;\"><br \/>\n<\/span>now we will find the area of the large rectangle is how many<br \/>\ntimes the area of the small rectangle as 22.2575 &#8211; 5 = 17.2575 cm<sup>2<\/sup>,<br \/>\nSo, matches with H.<\/p>\n<p>Question 13.<br \/>\nWhich expression is equivalent to 5 \u00d7 5 \u00d7 5 \u00d7 5?<br \/>\nA. 5 \u00d7 4<br \/>\nB. 4<sup>5<\/sup><br \/>\nC. 5<sup>4<\/sup><br \/>\nD. 5<sup>5<br \/>\n<\/sup>The expression which is equivalent to 5 X 5 X 5 X 5 = 5<sup>4<\/sup>,<br \/>\nmatches with C,<\/p>\n<p>Explanation:<br \/>\nGiven expression as 5 X 5 X 5 X 5 means 5 is multiplied by 4 times,<br \/>\nSo 5 X 5 X 5 X 5 = 5<sup>4<\/sup>\u00a0which matches with C.<\/p>\n<p>Question 14.<br \/>\nA walkway is built using identical concrete blocks.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27183\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-372.1.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 372.1\" width=\"645\" height=\"152\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-372.1.png 645w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-372.1-300x71.png 300w\" sizes=\"(max-width: 645px) 100vw, 645px\" \/><br \/>\n<strong>Part A<\/strong><br \/>\nHow much longer, in inches, is the length of the walkway than the<br \/>\nwidth of the walkway? Show your work and explain your reasoning.<br \/>\n<strong>Part B<\/strong><br \/>\nHow many times longer is the length of the walkway than the<br \/>\nwidth of the walkway? Show your work and explain your reasoning.<br \/>\nPart A :<br \/>\n\\(\\frac{11}{4}\\) inches in the length of the<br \/>\nwalkway more than the width of the walkway.<br \/>\nPart B :<br \/>\n2 times longer is the length of the walkway than the<br \/>\nwidth of the walkway,<\/p>\n<p>Explanation:<br \/>\nPart A :<br \/>\nGiven length as 5\\(\\frac{1}{2}\\) inches and width as<br \/>\n2\\(\\frac{3}{4}\\) of walkway. Now longer, in inches,<br \/>\nis the length of the walkway than the width of the walkway is<br \/>\n5\\(\\frac{1}{2}\\) &#8211; 2\\(\\frac{3}{4}\\) first we write<br \/>\nmixed fractions into fractions before subtraction as<br \/>\n5\\(\\frac{1}{2}\\) = (5 x 2 + 1 by 2) = \\(\\frac{11}{2}\\) and<br \/>\n2\\(\\frac{3}{4}\\) = (2 X 4 + 3 by 4) = \\(\\frac{11}{4}\\),<br \/>\nSo \\(\\frac{11}{2}\\) &#8211; \\(\\frac{11}{4}\\) ,now we make<br \/>\nboth denominators same as 4 so\u00a0 we multiply numerator and<br \/>\ndenominator by 2 for \\(\\frac{11}{2}\\)\u00a0 = \\(\\frac{11 x 2}{2 X 2}\\) =<br \/>\n\\(\\frac{22}{4}\\) ,Now \\(\\frac{22}{4}\\) &#8211; \\(\\frac{11}{4}\\),<br \/>\nas denominators are same we subtract numerators and write as<br \/>\n\\(\\frac{22- 11}{4}\\) = \\(\\frac{11}{4}\\) inches.<br \/>\nTherefore, \\(\\frac{11}{4}\\) inches in the length of the<br \/>\nwalkway more than the width of the walkway.<br \/>\nPart B :<br \/>\nNow we will find many times longer in the length of the walkway than the<br \/>\nwidth of the walkway as \\(\\frac{11}{2}\\) \u00f7 \\(\\frac{11}{4}\\),<br \/>\nnow we write reciprocal and multiply as \\(\\frac{11}{2}\\) X \\(\\frac{4}{11}\\) =<br \/>\n\\(\\frac{11 X 4}{2 X 11}\\) as both have 11 they get cancel,<br \/>\nwe will get \\(\\frac{4}{2}\\), as both goes in 2 we get 2 X 2 = 4,<br \/>\n2 X 1 = 2, (2, 1), \\(\\frac{4}{2}\\) = 2,<br \/>\ntherefore 2 times longer is the length of the walkway than the<br \/>\nwidth of the walkway.<\/p>\n<p>Question 15.<br \/>\nA meteoroid moving at a constant speed travels 6\\(\\frac{7}{8}\\) miles<br \/>\nin 30 seconds. How far does the meteoroid travel in 1 second?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-27185\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-373.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 2 Fractions and Decimals 373\" width=\"388\" height=\"108\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-373.png 388w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-2-Fractions-and-Decimals-373-300x84.png 300w\" sizes=\"(max-width: 388px) 100vw, 388px\" \/><br \/>\nThe meteoroid travels in 1 second is \\(\\frac{11}{48}\\) mile,<br \/>\nmatches with G.<\/p>\n<p>Explanation:<br \/>\nGiven a meteoroid moving at a constant speed travels 6\\(\\frac{7}{8}\\) miles<br \/>\nin 30 seconds, Now in 1 second the meteoroid travel is<br \/>\n6\\(\\frac{7}{8}\\) \u00f7 30 =<br \/>\nFirst we write mixed fraction as 6\\(\\frac{7}{8}\\)\u00a0 = (6 X 8 + 7 by 8)<br \/>\n\\(\\frac{55}{8}\\) now we divide with 30 as \\(\\frac{55}{8}\\) \u00f7 30 =<br \/>\nNow we write 30 as reciprocal as \\(\\frac{1}{30}\\) and multiply as<br \/>\n\\(\\frac{55}{8}\\) X \\(\\frac{1}{30}\\) = \\(\\frac{55 X 1}{8 X 30}\\)\u00a0 =<br \/>\n\\(\\frac{55}{240}\\), now both goes in 5 as 5 X 11 = 55<br \/>\nand 5 X 48 = 240, (11, 48) = \\(\\frac{11}{48}\\) miles,<br \/>\ntherefore, the meteoroid travels in 1 second is \\(\\frac{11}{48}\\) mile,<br \/>\nwhich matches with G.<\/p>\n<p><em>Final Words:<\/em><\/p>\n<p>Hope the details regarding the Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals pdf are helpful for all the students. Learn the concepts of fractions and decimals in detail from here. Feel free to post the comments if you have any doubts regarding any of the topics. Keep in touch with us to get the latest updates of all BIM Grade 6 Answer Key.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>It is very tough to clear all the math exams without proper preparation. The solutions in Big Ideas Math Answers Grade 6 Chapter 2 Fractions and Decimals are prepared by our highly-experienced subject experts after ample research and easy-to-understand concepts too. 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